I'm a cyclist of many hats (lol). Back when I didn't work and enjoyed life more I had a skate style helmet covered in stickers for BMX riding, a mountain/road helmet for my multi-hour MTB jaunts, and a full face style helmet for more serious DH and skate park riding. I tended to dump a lot of income into cycling and music back then...
I understand if it's not feasible to have multiple helmets, but if you can afford to have both kinds, you may as well. Then you can lend 'em to friends and such, even if you don't end up using them all time like I used to use/d mine.
As for the differences, the skate style works for BMX because it's a very anaerobic activity, you stop and rest a lot in between really fast efforts on the track, or jumps at the trails or attempts at a ledge or what have you. You can even take off your helmet while you're resting so the overheating issue is less of a factor. Full face DH helmets are the same. You ever see a DHer pushing her/his bike up to the starting line? They don't wear their lids because they're hot as hell. Giro use to make a helmet that addressed that issue for the free ride crowd called the Switchblade. It had a removable face guard. I saw a woman wearing one at a crit race one time. If your on-road trips to the market are short and you take your helmet off while there a skate style might suit you. If not I'd say to stick with your current style or maybe find one that 'bridges the gap' like the more serious MTB styles like the Giro Xen and Hex (I think Bell has some similar designs, but I'm not familiar with them since I haven't shopped for a helmet for several months).
One last point: I think the "helmet looks perched on top of the head" is a sign that the helmet doesn't really fit. When I try on a lid that does that I tend to keep looking; but, then again, I am incredibly picky about things that are to be worn on my body.