what's better: slow or vigorous fermentation

All else being equal (assume two identical recipes, identical ingredients, identical fermentation temps, etc. etc. etc.), what kind of fermentation is better, one that proceeds slowly or one that "burns out" rapidly? Which would produce more ABV, which more residual sugar?

I haven't done wines in years. My experience, in general, has been that a slow ferment means higher residual sugar. Fast ferments tend to rip though everything and end up dry. With equal starts, residual sugar means lower ABV.

With Wine you really want to ferment as slow as possible. This will make for a much better quality wine at the end. It is true that you will end up with more residual sugar but I can normally get my wine down to 990SG which is very dry so there cant be that much left. I normally ferment for 3-4 weeks.

So is there any way to affect this. Keep it cooler? My first wine is making my airlock look like the water in it is boiling. It's going crazy!

Slow is always best and can be controlled by the temperature.
Generally speaking reds should ferment at a slightly higher temp than whites which need to develop the fruity esters required in white wines.
The worst possible place to ferment any wine is in a airing cupboard as the temperature fluctuates so dramatically.
No wine should take less than 4 weeks to ferment out properly, any faster and off flavours will develop during the maturation.
Hope this helps,
TC