There was a wonderful writeup by someone on the exact manpower rest and redeploy requirements of having a few Crowsnest Helos vs a couple E-2s elsewhere not long ago. Extremely detailed, good in thought (at least seemingly) that showed the difference isn't that gigantic.
E-2 clearly has speed, range, endurance per launch, but only two platforms doesn't give it a lot of robustness in terms of maintenance losses or (worse) a combat loss. However due to its longer missions, if kept stable they can maintain good coverage.
Crowsnest is more flexible in its output but required more aircraft up and about to perform the same duty. Thankfully you can fit more aircraft, and exchange kits if you really need to, or launch/repair it from other vessels.
Swings and roundabouts. In the end what it came to is that E-2 has a greater offensive AEW capability due to the range/speed, but that Crowsnest has a greater depth and flexibility. If the CdG were in refit, then the French would lose all AEW entirely.
Of course, this comparison goes out the window if you consider 4 E-2s off a Nimitz/Ford, but thats outwith the scope of the comparison.
In short - Not that big a difference on the scale the UK/French work at, just differing flavours. UK's solution much more defensive though.