Forza
Pros:
Great graphics and detail.
Large variety and quantity of vehicles.
Great community.
In-depth photomode which allows endless possibilities.
Best livery editor I've ever seen on a racing game. (Franchise in general)
Great choice of tracks.
Cons:
Driving physics take a while to adjust to. Seem quite clunky compared to previous titles.
Lack of content present in previous titles such as FM4. (Example, Storefront / Auction House)
No day/night cycle or weather cycle. Night / rain only available on select tracks.
Weather system is IMO the weakest between Forza, PC and DC.
Driveclub
Pros:
Better graphics and detail.
Fun Factor with the driving.
Great community.
Full day/night system and weather system which allows you to fully customise conditions on any track.
Well priced DLC.
Points based system to unlock cars. No currency.
Great choice of locations.
Cons:
Severe lack of car variety mixed with a small quantity of cars.
NO CLASSICS!
Weaker photomode. Doesn't allow for the creativity of Forza.
Fun factor wears off after a few months.
Livery editor is quite basic.
In terms of photo quality when uploading, while Driveclub's version is much simpler, Forza's provides much less compression resulting in higher quality photos.