Triple tends to be mainly used on mountain bikes or on lower priced bikes such as hybrids etc..
Triples can be found on top quality frames and component groups.
All three rigs have their pros and cons.
The triple and regular double usually have the same big chain ring size therefore the rider will be able to pedal at a faster speed without "spinning out". For me, I usually coast once I hit 40-45 mph, but I feel more comfortable using a full sized big ring as I approach 40. Only significant for those that actually try to pedal above 35-40 and/or dont' tolerate pretty high cadences. (I don't really feel comfortable pedalling about about 110).
The compact has 1-2 lower gears than the regular double, but the triple has 1-2 lower yet. Only significant for those that need them of course, and there are no generalizations in that regard.
The triple has a very slight weight penalty. Probably on the magnitude of a couple of ounces.
Shifting- here's the big controversy. Most (all?) agree the regular double shifts best. Many say the compact shifts better than the triple, but I've never found that to be true. I feel all can shift flawlessly if maintained properly. There might be differences, but if so, I'm doubtful they're relevant anywhere except in a very tough racing situation.
One advantage of the triple compared the compact to many riders is the versitility of the middle ring - useful across the entire rear cassette and often results in far less front ring shifting, thus negating any perceived disadvantage or actually making the front shifting "better" in aggregate. It is often more versitile than the (usually identical) small ring of the regular double because of the middle position and the chain line it results in.
Many report that compacts with their large jump between the big and small ring, results in more front shifting, more "double shifts" to move smoothly up or down the gear range. In this regard, the triple and regular double are usually identical to each other in the two largest rings, with just the third, small ring added to the triple. Therefore, regular double and triple will have identical shifting between those two rings.
When I ride my 52-42-30 triple bike with similarly strong friends on 50-34 compacts my shifts in the low rolling hills are much smoother because I'm just shifting on the cassette while they far more often have to shift the front rings and then shift one or, often two, cassette sprockets to get the even progression in shifts. Much more fiddling and much less smooth in the paceline.
My editorial comment is: my personal believe is that compact doubles are just a camoflage and at best a compromise for those that need lower climbing gears but for style or perception reasons won't ride a triple on a top end road bike. To me, it's like a balding person using a comb-over rather than just saying "screw it, I'm bald, who the F cares. It's much easier just keeping the hair short all around." There are reasons batted about that a compact is actually "better", but I haven't heard any that are objectively true or actually meaningful.
Again, everyone should just choose what set up they really need. Pick the one that serves 100% of your needs. My fear is that the popularity of compacts will make good triples harder to find, which is not a good thing in my opinion. I would never settle for a compact double by choice.