First up the bigger the number of mm the longer the lens so a 300 is longer than a 200.
However a 70-200 has a wider maximum apperture (f2.8 as opposed to the f5.6 of the 70-300) , this means that you can fit a 2x teleconverter and make it effectively a 140-400 f5.6
However although the 70-200 is a cracking lens its expensive and thats not the route i would suggest if you only want a long lens.
PersonallY i'd say just buy a longer lens , depending on how much cash you want to spend there are multiple options but the likeliest options are
if you want a zoom:
sigma 150-500 OS
Sigma 50-500 OS
Canon 100-400 IS
alternately if you want to spend less you could look for a non stabilised lens like a sigma 170-500 or 135-400
second hand
or if you want a prime (that is a lens with a fixed focal length)
I'd suggest a Canon 400mm
I'd be careful about buying sigma 400mms
second hand as a lot of the older ones don't work with DSLRs , and id suggest staying away from mirror lenses which although very cheap are foixed apperture and limiting.
In terms of where to look , as you can't yet get in the classifieds here I'd suggest if you want new you look at kerso's site flashcamera.co.uk , at panamoz, at Digital rev, or Hdew , while if you want second hand I'd recomend MPB, Mifsuds, camtech, or ffordes