I managed to get a lot of time with my cousin's GS4 (T-Mobile) and brother's Maxx (Verizon) for roughly the entire day. The GS4 did have Nova Launcher skinned over TouchWiz or whatever Samsung runs on their homepages. First thing is, I didn't consider trying to find an HTC One to play with as my co-worker has one and showed me the "death grip" on it where the signal strength would diminish depending on how you hold the phone; even after an exchange, the same problem persisted.
Personally, I don't think you can go wrong with either phone depending on your preferences. I do like the always on Moto Assist even if I hate hearing my brother say "OK Google now" all the time as it just comes off as free advertisement for Google. Not sure why this bothers me, but it does. Aside from that, way the screen flashes when there's a notifications and easy access to read them is nifty. The screen also flashes periodically if you have pending notifications. The only gripe I had was having to press the send button to reply/send a text message. I cannot compare this to Samsung's S Voice as I didn't get to use it.
The quality of the screen is about the same to my eyes. I could honestly not tell the difference between the 1080p Pentile vs the 720p RGB where I did want to like the Maxx's screen more but objectively cannot say that it is any better or worse. The speaker quality was a little louder on the Maxx. Where the GS4 has a clear advantage is the camera. The Maxx was much too inconsistent and really just plain sucked. Some pics were nice, some were just grainy or not crisp/clear. The GS4 was far more consistent at taking pics. This was taking pics with both of the same things at different light settings at different times of the day. I cannot comment on the battery as both were at different charge levels, and I wasn't paying much attention to it. I think it's safe to say that the Maxx will likely be way ahead of the GS4 on this front though.
As for the UI, again, Nova Launcher was on the GS4. Some made it seem like this phone was super laggy, but it wasn't all that laggy to me. Navigating through the phone was easy with no hiccups or anything like that. There is a slight delay but nothing that was frustrating or even really noticeable on a non-OCD day to day type of use like flipping through screens, opening an app, or taking pictures. With that said, the Maxx was a tiny bit more crisp with webpages maybe loading a hair faster. I don't think there's a whole lot separating the 2 on this front unless you have a ton of apps running in the background, or you have some battery hogging app that's really tying you down.
I can't comment on the quality of the signal either. I'm just going to assume the Motorola is better able to find and hold a signal based on users of both Motorola and Samsung. I live in SF and we were hanging out here. Signal strength was never an issue. I didn't use GPS on either phone.
Verdict: If you live in an area with good signal like I do in San Francisco, I think it'll come down to valuing the camera or battery life. Samsung just has some gimmicky crap where you can just appreciate the Maxx for its simplicity. But the Maxx's camera is garbage. I don't care if someone says to just carry around a point and shoot. Many of us don't lug a separate camera in our pockets but rather use our phones to take photos.