I find it very unfortunate that this site is not updated anymore
http://coh2chart.com/
from there it was pretty easy to get an overall impression of the dominant factions in every game mode and skill bracket.
"Unfortunately, Relic hasn't been able to update their database since 16.5.2017."
Considering this data hasn't been updated in almost a year and we've had at least 3 decently sized patches in between that time I wouldn't consider this reliable in determining what the balance is like in 2v2 atm. It would be better to compare what tools were most effective during that time and today.
In all honesty though I find in 2v2 whoever can tech up to t3/t4 vehicles faster and camp the VPS well, while also continually forcing your opponent to fall back and have mp bleed will be in an advantageous state. It all comes down to area lockdown and strategically outpacing your opponent. I find with allies it is determined either by camping VPS early and hold both sides or one large side of the map, and with axis, being able to bleed allies faster with indirect fire and elite/vet units without getting suppressed or bled in return. I agree with Cruzz that certain maps are more effective for axis in the long run, but I wouldn't say it's impossible or highly unlikely for allies to win on those maps. It all comes down to the major engagements mid-game and the ability to bleed your opponents mp/resources/vehicles/and VPS. At the lategame stage it really comes down to how well you use your armor and arty to counter your opponents exact arsenal while also retaining more inf. If you lose the first major vehicle engagement more often then not, you lose the game, unless you throw your advantage to well positioned AT afterwards. I find with allies it's more so they win if they can overwhelm axis effectively mid-game(unless they allow axis to recover in lategame). With Axis it's more so can they keep their armor alive and prepare for the effective dive rush killing allied armor in a decisive engagement after arty and inf has damaged their defenses.
In conclusion I find it is a little easier to come back with Axis than Allies as Axis vehicles have better AT capability as long as they're not picked off 1 by 1 but push in a combined push(stugs/jp4/p4s/jadgtiger), and axis arty can decimate allied at-guns more effective in 1 salvo(as opposed to raketens which can sometimes escape if retreated in time) pak guns also can get away if arty misses during 1st salvo.
As a side note IL-2 and P47 seem to be slightly more effective than JU-87. Especially since ostwinds have a hard time shooting down p47/il2 while flak hf can shoot down il-2 but not P47 if it targets the flak(unless it's vet 3 or above). So I feel IL-2 may need either a suppression or dmg nerf. While P47 may need debate on what should be changed.