I think it’s a really interesting set of options, and one that will naturally lead to different Shepards choosing very differently. There’s no purely correct or incorrect answer, from a moral standpoint, which was why I thought the endings were pretty good in concept even in the pre-Extended Cut version (although their executions are all greatly improved in the EC). Every choice comes with a significant price, and it’s really a question of what your particular Shepard considers the least objectionable combination of cost and benefit - and what your Shepard even considers “cost” and “benefit” will vary depending on how you’ve played him/her.
Destroy seems to be the most popular choice, but carries with it the price of murdering all extant synthetic life - which we’ve just spent three games establishing as every bit as sentient and worthy of protection as evolved “organic” life. So you can truly fulfill your stated mission, but at the cost of becoming a mass murderer. I’ve seen the “but they’re machines, we can rebuild them!” defense of this choice, but building a new AI is not the same thing as replacing the old, any more than cloning a dead child replaces the original.
The virtue of Control depends on your particular Shepard, and how much you as the player trust him or her to keep the galaxy’s best interests at heart in the coming millennia. If your Shepard is pure Paragon, this is arguably the “best” moral choice, as ParaShep is someone who deeply understands that with great power comes great responsibility. He/she has had the option to do terrible things for his/her own personal gain, and has always chosen the high road. Such a Shepard controlling the Reapers could be reasonably expected to do the same (and indicates as such in the post-game narration). Renegade Shepard, on the other hand, would gladly use the Reapers as a means of effectively taking over the galaxy - and says as much, in his/her version of the post-game Control narration.
Synthesis is the choice you take if you (however begrudgingly) admit that the Catalyst has a point. In the Mass Effect universe, history indicates that synthetics and organics will inevitably come into conflict. Javik himself, the biggest Reaper hater of them all, agrees with the Catalyst that synthetics have a fundamentally incongruous view of the universe from organics - whereas organics evolved naturally, and thus do not know/ need to know “why” they exist, synthetics know they were designed and constructed. This creates both a sense of purpose and, for truly individualized AIs, creates the biggest existential quandary imaginable. I get that lots of players find the idea that the Starchild is “correct” in his assessment of the situation repugnant, but the fact is that it’s borne out by the literally millions of years of history established in the ME canon. Peace between quarians and geth is the only data point to the contrary, and at the point in which Shepard encounters the Catalyst, it’s more of a nervous cease-fire than a true peace of any sort. So it’s actually fairly reasonable for a given player to decide that Synthesis is only way to resolve the conflict. There’s a reason why this choice is the 2nd most popular one, after “Destroy.” The cost, of course, is that you’re rewriting the genetic code of every life form in the galaxy without their consent. And it’s a serious one. But then again, forcing change upon the beings of the galaxy (usually against their will) is sort of what Shepard does - and one could argue that this is no worse than choosing, in Destroy, to end the lives of billions of synthetic beings against their will.
Refusal is the option with the most obvious cost: everybody you know and love dies horribly. But we learn that the next cycle does defeat the Reapers, and it’s strongly implied that they in through conventional means (i.e. no Crucible at all). This, not Destroy, is the choice of the *true *no-compromise Shepard, the one who takes it as self-evident that the Catalyst is not to be trusted. Such a Shepard would rather sacrifice his/her own civilization than give the Reapers an inch - especially knowing that Liara already went through great effort to give the next cycle clear, understandable information about who the Reapers are and what their military capacity comprises.
Regarding my personal choice… My true-blue Paragon Shep picked Synthesis, but strongly considered Control as well, since he knows he’d only use it for the common good - indeed, the moment there was any indication that he had overreached his authority, he would voluntarily self-destruct the Reapers himself. My Renegade Shep will almost certainly choose Destroy, since he never believed that synthetics were “alive” in the first place. Hell, he destroyed the geth heretics and sided with the quarians against the geth already. He, too, was tempted by Control (albeit for more, ah, ambitious reasons) but ultimately decided that he’d rather go out with a spiteful bang than have to babysit the galaxy for the next bazillion years.