Jerry - the GE HD is a great scope. If you can live with the reticle choices (I would suggest the ECR-1), it should work very well as a BR scope for your .22lr. The optics may show some minor aberration as the mag approaches max power. The turrets are pretty good. The elevation/windage travel values (55/45 MOA) are good. So the GE HD has plenty of mag, good glass, is not hideously expensive, and has many satisfied users.
IMO - the Competition has the better glass. It's not night/day to me, as I generally like Vortex glass, but the Competition glass is better. There has been a lot of talk here about the Competition's erector spring assembly and possible reticle movement. I have had no problems with mine whatsoever. It will cost new about $900 more than the GE. The Competition turrets are great, it has the same elevation and just a tick more windage travel than the GE HD (55/50 MOA). It's a very good scope.
FWIW - I put a NF 12-42x56 BR scope on my modified CZ455 .22lr rifle and have found it to be plenty of scope, although I didn't use a canted base and have limited elevation travel with it. With a 10 to 20 MOA base, you shouldn't have issues with either one of these scopes. Either one of these scopes has plenty of mag, reasonable elevation/windage travel, good glass, etc. IMO - the final choice would boil down to the difference in glass as seen through my own eyes, which brand of scope had the reticle I liked the most, and the difference in price, which is substantial. But you won't go wrong with either one.
For the intended purpose of BR, you might also want to consider some other options. For example, the Kahles 1050 scopes get very good reviews, and Nightforce, IOR-Valdada, and several other manufacturers also make fixed power scopes in the 36X to 44X range that might also be good choices for your described application.