I, too only have brief in-store experience with the S4. Compared to my Thunderbolt, it flies and is superior in a couple of the ways you might mean "speed." First of all, the Maxx is more responsive. I had been having horrible lag on the TB for simple tasks, like waiting for the phone dialer pad when I hit the phone key. Not a hint of lag yet with the Maxx.
Second, the network speed is better. I had been getting terrible speeds over the LTE Network, and my speedtests on the Maxx are consistently better, but more importantly, I use the paid version of
Network Monitor Mini and I can watch the download speeds in actual use; they are consistently higher on the Maxx. Motorola's reputation for good radios seems to be well-founded. I also maintain 4G reception in places I was dropping to 3G.
GPS is faster, too. The Maxx receives both GPS and GLONASS signals so it zeros in faster and in more places. In addition, the GPS signal strength is higher using
GPS Test