As dissimilar as whiskey and vodka. They both are designed to meet the same end, but by different people with different perspectives and different resources to start with.
I have both. I like both. I'm keeping the Advents, but that's as much a function of value of the HPMs and lack of an amp that matches well with them as anything else (yes, I had one that sounded wonderful, but it went back to its rightful owner). Plus I'm emotionally attached to the Advents, my first speaker.
They sound (and feel) neat stacked together.
I hear the major differences in the woofer tone and response. The HPM woofer is carbon fiber, and has a more wooden sound - in a good way. The upper range of it sounds like a stringed instrument (especially the body, as was mentioned in another now closed thread) instead of the strings of the instrument. Hard to explain, but everything sounds more like a human voice.
It's also a little boomy in response, as has been discussed ad nauseum here. The "mid-bass hump" is increased response in the rock n roll bass range, around 60-80 Hz. Stands, tilting, and stuffed ports seem to help, but not eliminate that.
Maybe they're a little brighter too. No, they are brighter. Sort of like a loudness button: the top and bottom have a boost.
"Better" is always a bad question in audio. That's like asking which religion is better in a room full of zealots. Everyone will have their preferences, East/West coast, flat/contoured, 2-way vs 3+way, ports vs sealed. Best bet is to decide what kind of sounds you like, listen, and judge accordingly.