I upgraded from the Nexus myself, 3 weeks ago, no regrets at all. This is hands down the best phone I've used out of the box, ever. Normally by now I'd probably be on my 3rd ROM, but I have kept this thing stock rooted, because the stock experience is fantastic, root only makes the experience that much better. I've thrown everything I can at this phone and not even a hiccup; Waze, Gmaps, Play Music, text, or phone call all at the same time and not one hiccup.
The GPS is fantastic and it's never made me wait to get a lock on a satellite. Man I didn't realize the Nexus was THAT bad until I got this phone, instant satellite lock everytime.
The battery is the biggest difference you'll notice between the s4 and the Nexus. The Nexus can only dream about achieving the same battery life.
The screen, the best on the market in my humble opinion. The One gives it a run for its money, but the extra real estate it has takes the cake, and I'm a fan of Samsung's AMOLED technology so that doesn't hurt either.
Verizon is getting a few phones once your upgrade rolls around, and I highly suggest you check them all out. The only mysteries left are if the Moto X is coming to Verizon and when the Note 3 is coming out, at least that's all I know about. So you'll have I would say, a good 4 or 5 solid phones to choose from by the time your upgrade rolls around. However, if you decide to go with the s4, you won't be disappointed. It's been 3wks and I can still barely keep my phone idle.