In my studio I always use electronic drums (V-Drums). Candidly, I don't have a good enough sounding room (or a large enough room) to track live drums. However, I sometimes do add accoustic cymbals and/or hand percussion if the project demands it).
When I lay down tracks for other people (in other studios) I normally use real drums/percussion. Many studios have some type of "in house kit" (although I find the cymbals on most "in house kits" tend to be horrid). Although I feel my kits are often better than the kits provided, I defer to the producer/engineer (many times it's a matter of economics, since the kits may already be mic'd, etc).
If a studio doesn't have a kit - or doesn't have enough mics, channels, tracks, to properly record an accoustic kit, then I may suggest my V-Drums (it pays to ask plenty of questions in advance). If I do use the V-Drums I try to get the engineer to record the MIDI at the same time that we track the analog. This gives them options to trigger different sounds later in the project.
There are certian advantages to e-drums. You can record the MIDI performance and defer drum sound decisions until later in the project. You can also use virtual (MIDI) tracks to keep the analog/digital tracks free for more vocal, guitars, etc.
Although many people think e-drums just don't sound "real enough" I have heard plenty of e-drum tracks that were more than real enough.