little bit similar story as was mine. I got SGS (GTI-9000) before, rooted with CM10 JB was not really bad, but really not good enough (phone freezing a lot, often GPS lost...)
when deciding about replacement (august - september 2012) I ended up on choice between Samsung Galaxy S3 and HTC One X. I prefer Android over iOS, so (any) iPhone was not an option in my case. (I would not discuss iOS vs. Android in this topic, as per almost none experience with iOS.)
So, the choice was made: One X.
why? both are pretty similar when it comes to specs... reviews are mostly for S3, even OneX hits the top in some... but I found several important pros against S3:
construction: OneX polycarbonate (or whatever it is) body is way over S3 plastics. just play with both in store and you would feel the difference. although iPhone is probably the top in phone body design and construction.
display: S3 got Super AMOLED 2. Waze icons and bars were burned in on Amoled of my SGS1 after around 25-30k km. OneX got Super LCD2 instead. After around 15k km with OneX - no signs of burning-in yet. I think this is crucial for intensive wazing. (not sure about burn in problems on iPhone's display)
manufacturer's SW package: With old SGS I really hated samsung's launcher and mess around it (think it is called Touchwiz, or so, and samsung apps which are mostly useless garbage). so I purchased SPB Shell 3D for couple of euros for old SGS. With OneX I haven't even installed SPB Shell 3D as the HTC Sence is simply great. (I hadn't knew this before I tried OneX). (at this point - system openness and variability/customization options of Android are over iOS for me)
upgrades/support: after experience with SGS - software updates by Samsung were extremly late (late at least one major Android release, not even upgrading SGS1 to v4.0 or later), not really meeting users requirements (to have phone running fine, one had to use unofficial builds from XDA). HTC had better references (from colleagues and friends) when it comes to software updates and clearly stated that One X will be upgraded to JB soon (in september it was available with ICS, upgraded to JB by the end of november). This one is maybe irrelevant now when S3 and OneX are delivered with JB.
there were also few cons regarding OneX:
battery cannot be replaced - as far as I remember the only extra battery I got was around 6 years ago for my first windows mobile smart phone IPaq from HP. on SGS I was taking out battery often, but just 'cos phone hanged...
no slot for external SD card - who cares if you have 32 gigs build in?
now One X+ is offered by HTC. So, if I were you, I would add this to comparison too.
now to your questions. (As I do not have experience with iPhone, I cant compare with it, but most probably no major differences between 4S and 5) - but regarding OneX:
1. device stability - excellent. had one phone crash in 5 months (playing with Waze Beta version)
2. GPS performance and stability - excellent. GPS lock usually within few seconds (and I park car in underground parking lot). able to got GPS lock even inside bulding (not far from window), no problem with GPS perception with phone in the rear pocket while driving.
3. one thing I miss - I'm unable to run Waze in foreground and car blackbox app (daily road voyager or autoboy) in background (blackbox app just stops recording when switched to background). I hoped that with quad core with GB RAM this would be running without problem.