Either tire will require wider rims, at least 7" if you follow the manufacturer's rim width spec. A larger, heavier tire reduces acceleration. Because these diameters are about 9-13% larger than stock, your speedo will read low by that much (but it is adjustable). If you have an early 5th gear ratio, it will become pretty useless. The later (88.5+) 5th gears were about 9% lower and will work better, but neither will be good. A 4:1 transfer case offers about a 12% reduction in high range, so you can get back your engine RPM and highway speed in 5th gear. 31's need a bit more lift/clearance, around 3". The 9.5" tire width will fit within your fender flares, and NOT require wheels with reduced backspacing (unsure about the 10.5" tires). In Calif, I can get cited for tires sticking out beyond fender flares (but it rarely happens). Is most of your driving ON or OFF -road? How often will you really need that extra half-inch of clearance?
Edit: Oops! I answered assuming Samurai. The Sidekick has better tire clearance, so you should be OK with what you got. The tires diameters are so close, only about 4% difference, that I'd keep the 31's unless you really need to eke out the last little bit of freeway performance. The narrower 30's will have less rolling resistance and make for a better road vehicle. The reduced backspacing you already have on your 8" rims is likely to be adequate for your 31's, but check at full lock/stuff just to be sure. Good wheel tech site at
http://www.rsracing.com/tech-wheel.html Edit2: From what I can tell, the 4.24:1 Trackick T-case gears do not change the high range. 30's are 8% and 31s are 13% larger than stock, so one route might be to change R&P to the 5.83 gears. That way, your hi-range gearing could remain about the same as OEM and your speedo would be closer to correct.