Too big? That's relative. If you're used to an iPhone, then you may initially find it to feel pretty large. But, as with most, you'll get used to it. Maybe even love the size. I can't stand the tiny screen on the iPhone now, but I used to think the 4" screens were HUGE coming from my HTC Eris (3.2").
The screen is slightly saturated according to most reviews, but (and here's the key) it is adjustable and dynamic. You can tone it down or up to your liking. Don't think the iPhone can do that.
Most people seem to think it is an amazing display. Also pretty subjective depending on what you're looking for. The iPhone displays are considered by some to be low resolution in today's world. It's hard to compete with the rediculously high res screens coming on Android phones today. The S4 has a better display IMHO than any other I have seen.
Charge time? Depends on if it is being used, powered on or off, and what charger you're using. Being a universal micro-usb port for charging, I end up using other peoples chargers. Many of which are rated to charge at different amperages.
Never really timed it though.