I threw my "80" (65cc) engine on an expensive ~ mountain bike (800$) with good shocks. Once the whole thing was tight and solid, I rode it pretty hard off road. It's nice to know that grass and rough terrain are not a problem even with an engine at speed. I never found vibration was a problem, and I just stand up on my pedals on grass and dirt, so I guess you'd need seat post suspension if you wanted to stay sitting.
I mounted my engine solidly to a steel plate and u-bolted that to my mountain bike, because the down tube on my frame is oversized (probably a common mountain bike issue), but if you drilled the frame, you might encounter issues if you came down too hard on it. Also, if you're going over grass and dirt and bumps for any extended period of time, things are going to come loose. Even with locktight. So it does mean that i have to check EVERY SINGLE BOLT before and after i use it hard. Probably a lot of people do that anyway even with cruisers, but they could probably miss a check once or twice and get away with it. Not so if you're putting it through off road stress.
I can report that putting an engine on a mountain bike does not really take away any of its "mountainess" ie, comfy off road riding and the ability to take varied terrain. And it's HELLA fun to have the whole city as my playground, and not just the roads and paths. It's like a go-kart that goes ANYWHERE.
I guess the main thing is that mountain bikes have thresholds of expense. Your shocks are almost always going to be the cheapest component on the bike, so if you're buying from a dealer, test those. The bikes overall goodness will probably be comparable to their performance.
I have never put an engine on a cruiser, but i doubt i would feel comfortable riding one the way i know i ride my bike. These HT engines, in my opinion, cannot be used hard and kept pretty as well, so i'll never be riding one for looks. If you're planning on staying on the roads though, it's probably easier, prettier and more efficient to stock bolt an engine onto a cheap walmart cruiser that has gotten pretty good reviews from most of the people who seem to try them. If you all ready ride a mountain bike off roads and on, then don't worry about loosing that freedom once the engine's on. The resistance from the chain tensioner means that your lowest gear is more of an effort, but i've never found it that much harder to pedal the thing off road either. Just usually lack the willpower
Demosthenese