None, other than weight & balance, she will probably never notice the change.
Except the recoil. Sounds like your wife is pretty little...make sure she shoots a box of 12 ga before you buy one and she's ok with the recoil.
Personally I'd keep her in a 20 ga if she shoots it well.
I hunt ducks with my Browning Citori lightning 20 ga. Use 3" mag #4 steel and I drop birds just as well as guys with 12 ga guns.
Think about shells, not a new gun.
I hunt dove and upland game exclusively with a 20 and I've shot my share of ducks with a 20 gauge as well, but if its gonna be a dedicated waterfowl gun, I would advise a 12. The extra capacity of the 12 will help put more pellets in the bird. My 20 gauge load only has a 7/8th oz. of shot in No. 4. Its not the power that's an issue its the number of pellets hitting the vitals.
My outlander with a load of 1 1/4 oz. of 3" black cloud isn't bad at all....my 12 year old could shoot it.
A 12 gauge semi auto isn't nearly as robust recoil wise as a pump or O/U 12 gauge