In my experience, a well tuned GBBR will perform at least as well tuned AEG.
Range and accuracy depend on a LOT of variables; I've seen some gas pistols outrange AEGs. Knowing the platform you use (AEG or gas) and understanding how to upgrade it is vital in this respect: just picking one over the other, alone, won't do much for you.
All airsoft guns experience issues in cold weather: on GBBRs gas cool down when firing and lack of heat to evaporate the gas can be an issue. Co2 and MAPP/MAP-Pro help combat this issue.
For AEGs, certain types of mechboxes (notoriously upgraded V2s) are prone to breaking in the cold; batteries tend to drain a lot faster and underperform in cold weather as well, with some smaller batteries dying in a surprisingly short time (rendinging AEGs which can only fit those battery sizes almost useless). I've frequently seen players go through several guns in a day during winter games, with a third a more ending up being out due to their guns being down. The hopup rubbers on both AEGs and GBBs tend to harden up in the cold which adversely affects their performance.
GBBRs require more frequent maintenance, but are much simpler to maintain and have very few components: barring your gun getting run over by a car or something, the only things that can break is something in the trigger group, the bolt carrier group or a mag will leak. A spare bolt can be swapped in in less than a minute; on my WEs I can change out the trigger pack in 2-3 minutes. A leaky mag, toss it aside and deal with it later -- your other mags still work.
If anything goes wrong with your AEG mechbox, you'd better have a spare gun with you.
Also some AEGs let you swap springs quickly, but most do not. On a GBBR with an NPAS you can adjust the FPS fairly easily, so you don't need seperate CQB and outdoor guns.
I prefer GBBRs because they're simpler, more realistic, provide a much quicker trigger response (and ability to properly double tap), no battery issues, easier maintenance; I haven't found any difference in range/accuracy (really comes down to upgrades and tuning either way); GBBRs are water/adverse weather -friendly; it's possible to build a very compact and low profile GBBR carbine since you don't have to worry about wiring and batteries.