As far as I experienced untill now, ONE of the factors is (wood) maturation.
I'll try to explain why.
Your initial question was:
What proces or which components determine the strength of the bite of whisky?
(I assume you do not mean different distilleries, because that is another story.)
I heared stories from people doing their own (single cask) bottlings and they explained that not all casks are good enough for being bottled as a single cask. These labels often identify the cask number, date of distilling and bottling. Sometimes you even can see how many bottles this cask yielded.
As you know, hearing someone telling something is nice, but you should experience it yourself!
We are lucky for this experiment, because here's how you can do it:
Signatory came up with a range of Port Ellens lately, with cask numbers 5143 to 5148. They were all distilled on 09.08.1979 and bottled on 18.02.2002 or 28.02.2002 (casks 5147, 5148). See http://www.whisky-archiv.de/index2.html.
Take two of these and make a direct A-B comparison!
Alternatively, you can try the Balvenie 15yo because these are also single cask bottlings (but I compared with the Port Ellens).
You have all the parameters the same: distillery, distilling date, bottling date and probably warehousing (but that is nowhere clearly stated). I assume that since all the cask numbers are in a following order, they are matured under similar conditions.
What you notice immediately is of course the difference in cask type: plain oak (ex bourbon) is different from sherry. Not surprising.
But what if you compare two bottling both from oak or both from sherry? There lies the experience I made that came to the given answer.
There are many more factors, but this one you can experience yourself quite easily.
I personally wonder about seasonal differences (like summer vs. winter), but so far, no reactions yet. Perhaps now?