They're very different beasts. The Anton has a 14-cylinder BMW 801 D-2 radial, with ~1980PS at max emergency boost, versus the V-12 Jumo 213 A of the Dora of ~2100PS. It's heavier, draggier, and less powerful than the Dora, so it should accelerate and climb quite a bit worse. It's also rather sluggish at higher altitudes, unlike the Dora. As it reaches peak power below 6km with a draggier airframe, its top speed is a fair bit lower than the Dora. However, it's an older variant in general so you shouldn't expect it to be better.
It does however have an extra two MG151 cannons in the outer wing, so there is a greater volume of fire. It should also carry a great deal more A/G weaponry, which is probably the role you should employ it in. Roll rate is also better, but turn rate is inferior. Realistically it'll struggle against the P-51 and Spitfire, however a competent pilot will be able to use it well as a fighter at lower altitudes.
TL;DR - Anton is inferior in all but roll and firepower, and A2G capability.
EDIT:
The cockpit is more or less the same, but the radiator control is fully manual.
