I've done both, and I don't really find one to be any more 'complicated' than the other. With film, there's the bulk of carrying many rolls of film, and potential for x-ray or other hazards (though I've never had any troubles). WIth digital, you have to worry about having enough charged batteries and a place in which to charge them, a dirty sensor, and I suppose some kind of electronic failure (though you could also have mechanical failure with a film camera). I know that many will disagree with what I personally do on vacation, but I do not worry about backing up on a laptop/hard drive etc while I'm on vacation (if I were doing it for paying work, it would be a different story). For our last trip to New Mexico and Arizona, I had my M9 and some 8GB SD cards, and a couple of 16GB SD cards, and never felt like I was short on memory. Last year we were in France, and I had enough cards for the M9 to do over 1600 RAW shots (imagine how much film that would be!), and they fit in a small pocket in my camera bag. Three years ago we were in Vienna for Christmas and I took my SWC and my Contaflex TLR -- stupid to bring both of them in the first place, as I then had to contend with carrying both 120 and 35mm film, making sure that I kept the exposed film protected and separate from the unexposed film, etc, so it was a bit to juggle (not to mention the fact that the camera bag weighed about 20 tonnes with those two camera kits). Not really a big deal, as it was something that I've been used to doing all these years, but compared to what I've gotten used to with digital on vacation, it was somewhat more cumbersome. But then again, I just did a short trip with my Canonflex and a few rolls of film, and it was quite satisfying!
Here again, as far as digital goes, I think backing up is a personal choice (for vacation, anyways). I tend not to worry about it (ignorance being bliss, perhaps?), but that's just me. And just like Godfrey, I just checked an SD card that I took to France last year, and yep, the shots are still there.
Other advantage to digital is that you can have much more versatility in your choice of ISO's. You could be shooting in bright sunlight one minute, and then in a darkened church the next. And of course the ease with which one can switch from colour to black and white -- unless you're using a Monochrom!