I do both, and multiple methods, because every method has it's advantages and flaws. When monitoring lower, I find that certain things are louder or quieter in the mix, and when monitoring louder, certain things take a phantom elevation in the mix. That happens alot on my own mixes.....one friend remarked that he couldn't hear the guitars on a couple of tracks, but his setup is a ridiculously imperfect room, and if the guitars were any louder, they'd start to completely mask all the synths, background vocals, pianos, orchestral parts. I had mixed it so that there was a good blend of audibility at normal listening levels.....but if you put on the headphones and or turn the speakers up loud, the guitars definetely start to bury the vocals and background vocals, and that the sub 150 Hz on the bass drums really, really start to make themselves apparent.
In that sense, if you EQ things in a very specific way to not be overly compressed or limited, you start to almost have a couple different mixes--one when quiet, one when turned up. Especially when you have alot of different things in the mix, like soft melodic parts (organ, synths with the filters rolled off), loud guitars, orchestral stuff. I've noticed that orchestral stuff, if you don't have it as the dominant instrument in the quieter mix, will get fairly obscured by loud fuzz guitars when turned up. But I also tend to have a whole bunch of instruments and instrumentation going on in that not everything can be audible, i'm a big fan of non-essential additional obscured buried sounds that you have to dig for. This might sound funny, but when i'd dub tapes for friends at high speed levels, i'd be hearing instruments and parts that I didn't hear at the normal speed, where they started to take precedence. It's like the psychoacoustical properties of mixes change with environment, dB levels/ loudness, speed, etc.