XT typically has more features than Deore, and more refined materials/constructions methods.
The differences between the two is hard to summarize, and depends on the generations you compare, as some technologies that were exclusive to XT have arrived after some time to Deore.
For derailleurs/shifters, XT shifters can move 4 gears up/2 gears down in one stroke, versus 3 up/1 down for Deore. XT uses bearings in some places where Deore uses bushings (jockey wheels, shifter axle),... The shifter contact points is rubberized on XT,... There are other differences, but that gives you an idea of the kind of difference that exist between the two ranges. These are mostly refinements, that are noticeable, but are probably only critical in competitive environments.
On the question old XT vs new Deore, it depends on your priorities and the generations you are comparing. If you want a single chainring, no discussion, new Deore (6100 not 5100). If you want multiple chainrings for the range, old XT is probably a better option (Deore with double chainrings have as much range as a 6100 Deore single chainring).