I swear, everytime I am interested in a specific subject, a thread about it pops up here the next day...freaky!
I have been experimenting with the new Klanghelm dc8c yesterday (which is an AMAZING software comp imo), and it covers a lot of ground, going from very fast and snappy to round and smooth, from coloured to transparent. I've also acquired Ermin's book a few days ago, and in parts of the book, he mentions what type of compressor oftentimes works well for him on certain sources.
Because I don't own a few of those types of compressors, I have been trying to emulate what they do roughly with the Klanghelm, so I have gathered some info and listened to examples to find out what is typical about them.
Take it with a grain of salt, because like said, I don't all of these compressortypes. I'm basing some of the info on audiofiles and descriptions I've come across.
From what I have gathered, these are some of the more obvious differences between VCA, FET and Opto:
VCA: Typically can go from very fast/snappy/tight to smooth. Usually clean/low distortion (eventough you can force it to mutilate the signal). I've seen this type mentioned a few times as a "usable for everything, but better for some specific things that need fast action". Probably a good choice for catching fast transients.
FET: Also fast and snappy, but with more colouration. Oftentimes driven to high gainreduction for its pleasing distortion. Ermin describes it in his book as "Round and fat". The 1176 you mention is a good example of this.
Opto: Usually very smooth and gentle on the signal. Eventough not colouring, it imparts a certain vibe. Generally has a soft-knee behaviour. With some exceptions, they are seen as slower than their counterparts. Not necessarily because of their attackspeed, but because of their inherent smooth gain reduction curve. I think it was Bob Katz that called its response "sluggish". This style of compressor is very popular for vocals, where you might not want the compressor to clamp down too obviously.
Well, there's the result from my research last night. I would have loved to post some of the soundsamples I've heard, because they make these things much clearer, but none of them are owned by me. Just look for shoot-outs or comparissons between the more famous designs though, and try to listen for some of those things I've mentioned, and it will probably become obvious to you.