As opposed to creating a cover story that, if challenged, would bring more suspicion?
What brings this to mind, of course, is the Madeleine McCann case. Suppose for a second that the parents caused her death, but purely by accident. Perhaps they gave her Benadryl as a sleep aid, and never intended it to be fatal, but it was. What penalties would they face if they admitted this? Is avoiding them worth the risk of being investigated and, if it comes to it, being suspected of deliberate murder?
IANAL.
I don’t know - if that turns out to be what happened, they’ll still only be charged with whatever they have actually done, won’t they? (OK, the list of what they’ve done would have expanded to include conspiracy to pervert the course of justice or some such), but accidental death + attempt to cover it up does not equal murder (not that you were saying it did).
There is much in what Rilchiam suggests.
In my experience (limiting my observations to my jurisdiction, because local laws may change the equation) people who have been involved in a killing have a terrible dilemma to resolve. In simple terms, to prove murder, the prosecution has to establish an unlawful killing plus a guilty intent; to prove manslaughter, just the unlawful killing.
Thus, a suspect can adopt Plan A - stonewall and deny any involvement, with the risk that if something turns up (fingerprints, witnesses, etc) they are toast. It is (tolerably) easy to make the link between proof of presence at the scene + complete (false) denial equals guilt of murder. That initial position of denial pretty much shuts out all the excuses which are dependant upon the minutiae of the event such as self-defence, provocation etc - how can you say you were provoked if you weren’t there? And any later attempt at a fallback position has obvious huge credibility problems, which can make things even worse.
On the other hand, stone cold denial might result in getting off altogether if nothing turns up. There commonly aren’t other witnesses present; forensics aren’t as infallibly successful as CSI suggests, and so forth.
Or one can move to Plan B, and admit limited involvement, or some species of “confess and avoid” - the deceased threatened me, he provoked me, it was an accident, I was insane, etc, all of which may have different legal consequences but which at least have the advantage of such credibility as emerges from consistency of account from the outset, and the provision of evidence raising various matters of exculpation which would probably otherwise be absent (because killings commonly do not occur with witnesses present). Plan B tends to help enormously to avoid the risk of going down for the Big One, at the expense of possibly going down for manslaughter (and getting a lighter sentence).
As with all dilemma games, a suspect has to factor in things such as the presence of co-offenders and what they might say, and the price of various choices - in my jurisdiction, murder gets you mandatory life, manslaughter might get you around 10; less if you are lucky.
In summary, (subject to the observation that all generalities are false) if you deny all, then you make murder an easier call for a jury if the evidence starts to stack up against you, because intent is relatively easy to infer in circumstances uncomplicated by excuses. The prize, though, is a complete acquittal if nothing turns up. On the other hand, if you admit involvement, you buy a little credibility at the price of a likely conviction for at least manslaughter, and maybe murder if you do a rotten job of it.
Best way to avoid having to face this hugely tough call, of course, is to walk away before it gets to having to gamble with your life. 
Not to be a buzzkill, but by “better” does the OP really mean “liklier to stay out of legal trouble”? Because, of course, if “better” includes ethically, then the answer seems clear.
Assuming liklier to stay out of legal trouble, isn’t it a crime to interfere with the investigation of a death?
Another option (in the USA) is to maintain your silence and wait and see how the evidence stacks up.
All my Lawyer and Judge friends have repeated this: you should say only two things (if they are questioning you as a suspect, whether or not you are guilty) “I want to speak to my/an attorney.” “Am I free to go?”. Until you actually speak with said attorney. Do not think you can talk your way out of it.
While this is generally correct, if a family member of yours is murdered and you refuse to cooperate, the authorities will assume that you are guilty and may stop looking down other avenues for the “real killer.”
So if a family member of mine were murdered, I would cooperate 100% with the police on the condition that all my statements would be video and audio taped.
I meant likelier to stay out of legal trouble.
Informative posts so far. Noel, another question. What’s criminal negligence? Would that have covered the use of cough syrup as described in the OP?
I’m going to go back to Dr. Deth’s position: don’t say anything without a lawyer present. Once the lawyer is there, I’d be 100% cooperative, but I want someone in the room who’s there to represent my interests.
Obstruction of justice or interfering in an investigation or whatever it’s called in a particular jurisdiction may indeed be a crime, but since Americans have the right not to incriminate ourselves I would be hard-pressed to imagine a circumstance under which one could be successfully prosecuted for asserting one’s Fifth Amendment rights.
(Leaving aside for the moment questions of grants of immunity and the like which have an impact on said rights)
But Americans don’t have the right to lie. You can’t say you saw a one-armed man do it, and then it turns out that you did it accidentally. That would be obstruction of justice…
There’s also the question of your actions, which could up your jeopardy in a big way. You got home, hypothetical victim was motionless and blue. Instead of calling for an emergency team, you stash putative victim in a large plastic bag. By doing so you may have stepped over the line, and several hypothetical months later it could be difficult to determine whether the victim was already dead at that point.
Most places in Anglo-American jurisprudence have the right not to incriminate yourself, as does mine.
The issue I was addressing was not one of entitlement, but one of pragmatism. And yes, there is an option of shutting your mouth, but I didn’t understand the OP to be directed to that option. Bear in mind that most people in a police station are subject to very considerable internal pressure (let alone external pressure) to say something, anything, because silence seems (subjectively) so guilty. If they did it, they want to get out of it; if they didn’t, they want to say so. That is why judicious use of silences by an interrogator is a powerful tool - anxious people tend to rush to fill them.
On the issue of criminal negligence, much depends on one’s jurisdiction. In Oregon (a place where I do not practice) I am aware that a distinction is drawn between recklessness and negligence. Broadly, reckless behaviour is doing something when the prosecution can prove the defendant was aware of the likely outcome, and negligent behaviour is doing something where the prosecution can only prove that the defendant should have been aware of the likely outcome. (Please understand that reducing these issues to one sentence necessarily involves some errors of compression.) Offences differ, as do penalties, depending on whether one or the other can be proved.
In jurisdictions derived from English jurisprudence, the distinction is not typically drawn, and the test for criminal negligence is still in many places derived from a UK decision from the early 20C in which the court said that before a jury can convict someone of an offence via the concept of negligence, a jury must be satisfied that the negligence involved went beyong a mere matter of compensation between parties and was so pronounced as to amount to a crime against the state (not meaning treason, but meaning “requiring criminal sanction”). This definition has unsatisfactorily circular aspects to it, but is still used in various places.
Thus, criminal negligence is (generally speaking) reserved as a descriptor to distinguish ordinary civil negligence cases (fender benders, slips and falls, etc) where there are no criminal law consequences, from those cases where the behaviour is so neglectful that there are criminal consequences (firing a gun at a cow on a farm property and hitting a motorist passing on a road in the background in circumstances where the shooter was not aware of the passing car but manifestly should have been.)
As to the use of cough syrup, I can’t say. I don’t know enough about the evidence in the McCann case, nor do I know anything at all about the local rules, which can be radically different from Anglo-American jurisprudence.
In my experience as an investigator, this is what gets you, in a myriad of ways: did the other people talk? Are the cops saying they talked and pinned it on you? If so, are the cops lying to you? If they didn’t talk, can they continue to stand the pressure? Will they change their mind/get a conscience/find religion? What about next month, next year?
In any criminal enterprise of two or more people, it’s highly unlikely that all parties will be smart and silent forever.