Changing my rear wheel tyre from 26 x 2.1 to 26 x 2.0: what's the difference?
I am reasonably assured the larger tire will fit. As has been stated here before, bicycle tire width sizes aren't an exact standard. Maker A's tire size 2.0 inch may in fact be larger than Maker B's 2.1. The best information comes from user reviews about a specific model. Just to be sure look at your current tire. Does it barely fit between the frame stays? When on the smallest front sprocket how close is the front derailleur from hitting the tire. If the tolerances are very close the larger tire may not fit. Tire design also comes into play. A full knobby tire ( WTB velociraptor)  may hit while a microknob  (Geax AKA) may have enough clearance.