Like Eric said, the quality of the signal is what might impact your battery. WiFi is NOT necessarily better than mobile data, it's just usually that way, but if you router is too far away, it'll actually struggle more than mobile data and therefore, deplete your battery faster. 3G and H+ usually run in the same band, so your phone switching from 3G to H is usually just optimizing data transfer when it's doing something in the background. If you see it switch from 3G/H/H+ to Edge to 4G, then THAT does cause a higher drain as it jumps bands back and forth, and as usual, Edge is lighter on the battery than 3G/H+ and even more than 4G.
In some models you can go to Mobile Networks settings and select 3G-only if you want to save battery if you're in a crappy 4G area and don't really need the speed, but I believe some other models, like AT&T's, disabled this option for some reason.