You can get a range of magnifications with a single barlow by varying the path length between the barlow lens and the eyepiece (using focuser barrel extension tube(s)). I did a series of measurements on the UO 2" barlow (along with the Shorty Plus barlow; yet to write up the results for the site
). Typically I could get magnifications ranging from 2.1x to 2.9x depending on EP-barlow distance. View looks great at all mags.
More specifically, in answer to your qn, a good 3x barlow should be as good as a good 2x barlow. Yes it is big diff in magnification. For an 8" or bigger scope, atmospheric conditions ("seeing") will determine how high you can push the magnification before everything becomes a blur. If you are just starting out, just go for a 2x barlow and leave it at that. You will be able to use it with more EPs than a 3x.