Have you ever actually owned an HTC device...especially on Verizon? Sense is a much bigger battery drain than you think. Every phone they've released on Verizon had piss poor battery life at best. Even my Rezound with the EXTENDED battery barely makes 10 hours WITHOUT barely using it. Unless you're tethered to wi-fi all day, HTC devices have never been known for battery performance.
Go into a Verizon store and pick up an HTC device and ask about battery life and after they stop laughing they'll walk you to something NON-HTC to answer your question.
You would think that with the lowest resolution it would be better, but no, it won't. The Inc4G essentially has the same battery in the Thunderbolt has and that was terrible (i know, I had one). If anything, the S4 processor and ICS will add a little extra life, but every time HTC gets new hardware they always make sure that sense gets "heavier" so battery life on their devices never actually grows. It just stays the same across all their products.
Even with that said, there are a lot of fans of Sense (in terms of looks and functionality) like myself that will like the non-gargantuan size of the Inc4G, but after having an Incredible, Thunderbolt and now Rezound, each of which with poor battery life and the fact that Sense just simply slows down the phone too much in terms of memory, I've had it with HTC and am looking forward to my S3 arriving next week.
Now, if HTC had essentially made an S3 in terms of hardware then I'd say Samsung has something to be worried about. Sense really does need 2GB of ram sadly. Their hardware is always top looking and good looking, especially the One X, but they'd need to have much more storage than the 16gb non-expandable they gave AT&T and then finally they'd need a better battery cause they are horrible at that.
If HTC took a One X, corrected those things above and then gave it to Verizon, Samsung would be worried. But, until then, there's a reason Samsung outsells HTC handily and also why the One series isn't selling as well as you'd think at AT&T (I work for AT&T).