I am by no means a tire expert, but I drove a Liberty with SR-As for a couple of weeks prior to getting my current Liberty which just has the STs. There's definitely a difference in feel... the SR-As just feel "bigger" and perhaps just a little "rougher" and I think they bounce a little more. But all of that should be expected as they are all-terrain tires.
For what it's worth, I decided not to upgrade to the SR-As because a lot of people give them bad reviews. I figured, if I want to upgrade the tires later anyway, why pay the (approx $229) difference to get the SR-As which I may not even like? I'll probably stick with the STs for a while until I build up enough "political capital" with my wife and then get one of the other brands you've mentioned. People seem to like both of them a lot.
2005 Jeep Liberty Sport 4x4, Patriot Blue/Medium Slate Gray
3.7L V6, Auto, Package 28C, Tow Group, ABS, Selec-Trac, Trac-Lok
Husky Liners F/R, Mopar Cargo Tray, Cargo Cover, Tire Cover, etc.