Well, sure, native is most often better than emulated (barring graphic and sound improvements, such as many emulators offer), overall, although a big phone (or a tablet, for that matter) = WAY bigger screen, for one thing. You also definitely need a somewhat beefy CPU/GPU combo to run most PSP games w/o any perceptible lag, so of course YMMV. I also tend to prefer PS1 games, to be honest; the PSP pickings can be a little slim, and I literally have every NTSC PS1 game that I care to possess (so no “Barbie Dream House 2” xD). But I play Disgaea often enough on PPSSPP, and it works fine; Disgaea, even though just a JRPG, is actually pretty hard on PPSSPP’s capabilities, and is a good test for any given phone.
The S7 has a relatively large battery, but “extended”…? Dunno. It’s a 3000 mAh battery, so take that as you will.
I own the Moga Power Pro 2, specifically, and it has a ~2330 mAh LiON battery, larger than any other internal controller supply I have seen on the market. It comes with a stubby little USB cord to connect it to your phone as an assistive charger, yes, although this won’t work if the controller is under a certain charge (1/3 or so?). Generally, IRL I can use the combo without hooking it up this way for at least 2-3 hours of continuous play, if both start with a full charge. The controller will last MUCH longer than the phone will. Used as my main PC controller, I end up charging it every 1-2 weeks, depending on use. Yes, it will fast-charge if your charger has the amperage, and yes, it is usable while charging.
It’s in an XBox 360 configuration but that works fine for PS1/PSP games, as well, and imo the ergonomics are pretty good; it’s at least as comfy as the standard 360 controller. The only real caveat I have is that I wish the clamp that holds your phone (it comes with a separate stand for tablets, or if you just want to put your phone on it) would go a little further back, for a wider range of motion, as well as hold tighter, so you can play while lying on your back w/o it moving; I use a rubber band for this, so +shrug+ w/e, but it would be nice.
The fit and finish have been top-notch, so far; it doesn’t feel even remotely “cheap” or fragile. I have hardwood floors and so far, it passes the “bounce across the room” test with flying colors, when I get a little overenthusiastic while playing “Castlevania: Symphony of the Night” =x .
An additional nice feature, is that you can use Moga Serial directly with vJoy as a generic controller, so you can fully remap every button and/or axis, as well as use the lower shoulder triggers as digital buttons, both of which are often necessary for older games. This does, of course, remove all 360 emulation features ^^’ .