I prefer mics over triggers any day, simply based on the simplicity of mics. Place them where they sound the way you like, mix them and you're done. No need to worry about, sensitivity, crosstalk, etc. Triggered sounds can be altered to taste, so I wouldn't consider them to be inferior based on sound alone.
However, recently I have been experimenting with my drums mic placement for recording. I don't have a great kick drum mic, nor do I have extra cash available to buy a nice one (I recently bought all new cymbals). As a result, I wasn't getting a great kick drum sound that satisfied me. I almost got a better kick from just the overheads alone than from the kick mic itself. But I do have a full set of acoustic triggers and an electronic drum set with a module already on hand. So last night, I placed a trigger on my kick, through the module, and into the board. I dialed in the sound that I wanted, adjusted the pitch to match, and let 'er rip. This was a great solution for me considering that all I really needed was the fullness and beefiness that a good kick mic would have provided. I mixed in the triggered kick just enough to provide the fullness, along with the nice tone that I got from my kick through the overheads, and the result was very satisfying.
So to answer your question, yesterday I would have answered mics only. Today I have to answer that a mix of both mics and triggers opens up many possibilities.