I combine them all the time. Actually while waiting for the Mythic tier to ship, I took a scan of the original classic board and had it blown up (so the squares were 1x1 inch as the new one was supposed to be) and had it professionally printed (as a quad fold) via BoardGamesMaker. I use that on all my streamed games.
I use the remake furniture and tiles whenever possible, but also mix in classic style figures (along with some custom tiles) for variety. None of the classic stuff really looks out of place on the remake board. Some people will say stuff is "crowding" but that's not strictly true. The MOTM/ROTDM furniture tends to be slightly bigger (takes up more room on the board) but keep in mind that the remake Game System furniture is often actually SMALLER than the classic era cardboard+plastic furniture. So it fits fine.
Where you get crowding are with the default Abominations. They have the one hand reaching forward and the spear jutting out the other way. These guys will crowd you no matter what board you are using (especially when they are crammed into one of the smaller rooms). I have even favored using the alternate Abominations (Mythic tier and SQT/PoT) to make this a little better. Having monsters that are slightly different sizes side by side is no problem. You can use the classic heroes with the remake ones too (though when are you likely to have two barbarians together? I guess you could make one an NPC but even that isn't necessary).
If someone owns both classic and remake, I would not be afraid to mix them together. Maybe at first someone will nitpick but they will quickly get over it as the game gets going. It's like having a few painted characters but most unpainted for another example. I don't care if the bases are different shapes, it's all good because so much of the game is your imagination anyway.
Maybe someone will be worried about putting the remake assets onto a classic board, but if you have that you most likely have the bigger board. I HAVE heard some horror stories about the flimsiness of the Haslab version's board (ripping in the middle). I actually haven't yet used it for a game, I've always used this larger sized classic board instead (I printed it with matte finish so it wouldn't reflect back at the camera like the other shiny surfaces). I like having the "boot tile" On there, it's fine.
