I believe I have been in each situation separately and the effects are a bit opposite. One gives you the edge, sharpness and anxiety, the other relaxation and sleepiness.
So, assuming all the liquids stay down there, what happens?
Caffeine may mitigate the sedatory effects of alcohol for a bit, but if one continues to consume both, the sedation from alcohol will eventually overwhelm any stimulation from caffeine.
The possibility of death from acute alcohol poisoning is also increased, by a small amount, by adding caffeine. The extra alertness may allow the drinker to consume enough alcohol to kill them. Depends on rate of consumption, plus habituation effects from both drugs, if they are used regularly.
Short answer: Alcohol “wins”.
It also seems like it would take you longer to get drunk if you were alternating the two beverages. Similar to drinking a glass of water for every alcoholic drink you have. Also maybe less of a hangover.
The old caffeinated malt liquors (or were they alcoholic energy drinks?) like Sparks and Four Loko ended up being effectively banned, although I was never really all that clear on whether there was a genuine health issue or if it was just that they were very popular among underage drinkers and there was a bit of a moral panic over it.
Yes, I wonder if Irish liquor doesn’t have any effect other than placebo?
Still alcohol and coffee, even in the right proportions, don’t annul each other, I guess. Alcohol supposedly induces social interaction so I reckon someone drunk plus caffeinated would be really keen in having quick efficient social interactions with whomever.
Work would be done purposefully, with focus, but in the wrong direction.
Speech would be slurred, but over-articulated.
Sex would be slower, but acrobatic, fuzzy but sharper.
What else?
Many vodka and red bulls make me act like a straight up sweaty hyper jackass. And terrible hangovers. Though that could be because of all the sugar in red bull. My wife disapproves. YMMV
I remember thinking once that if Coke & Rum was good, Jolt & 151 Rum must be better.
I was wide awake with a hangover at 3 am.
Oh yeah, I remember thinking that same thing one time. My experimental results were quite similar to yours.
I can’t think of anything else besides sharp fuzzy sex now, and I blame you! 
The redneck’s speedball. If that isn’t a term it should be.
According to the CDC, it’s really not a good idea to mix caffeine and alcohol:
Biggest problem seems to be that the caffeine makes the drinker think they aren’t as drunk as they are, so they drink more and then do drunk stupid things.
Coffee may partially mitigate alcohol-induced liver toxicity (key word here is partially, it’s a matter of balancing risks and probabilities):
Real answer was given in first response.
So I feel free:
“You get a wide-awake drunk”.
An ancient gag. Recycled here for the edification of the youth.
I recall years ago reading an article about sensible drinking. With regard to having a coffee to “sober up” after a drinking session the article warned, “rather than being just drunk you will now be an alert drunk.”
If sharp fuzzy sex has anything to do with furries, I really don’t want to know. Some ignorance should not be fought.
No. Alcohol & caffeine are both diuretics. Maybe not some of the hangover symptoms but the headache from dehydration? Oh yeah, because both things you’re drinking contribute towards that.
Not so much a gag as a caution to believers in the ancient “give a drunk coffee to sober him up” myth.
Yeah, that furry stuff is out of bounds. I don’t care if it is Uma Thurman and her clone in a three-way. That teddy bear suit is just… Out…