I'm well and truly on the fence about either the HTC One or the SGS4.
I will mainly use the phone for looking at long tracts of text and although I could accomplish that quite happily on my SGS2 or even my SGS3, it does seem the screen on the HTC One will be better. That's a consideration for me.
Battery life is the big thing. I have heard rumours regarding battery life but I choose to ignore them until real world stats start to come in from those that have used the HTC One for protracted periods of time.
The manufacturers guidelines for battery longevity rarely, if at all, ever hit the mark.
I have also heard a rumour of a Samsung Galaxy S4 Duos with dual sim card slots (leaked Chinese pics a day or two ago showed dual sim slots). That right there is the clincher for me. I spend some of the year n the USA and some in the UK and currently carry two phones with me as I need to be reachable on either number. Being able to put two sims in an S4 would seal the deal right there.