I've never played it with a full server, so as usual, take my comments with a grain of salt.
In general the first half feels like an old school shoebox map, narrow, linear and confined. Where since there are few options, success becomes totally reliant on out shooting the guys who camp the same spots instead of trying to outwit them as well.
A cap can often be a slaughter for the Allies because of the open terrain, more cover coming out of the spawn towards the bridge would be helpful. I've never seen actual fighting on the bridge itself and since the river is so flat and shallow, it never seems that important. Usually, some axis run up on it and are quickly shot off, same for allies. You can cap A from behind the big rock on the left side, so that seems to be the anticlimactic way of accomplishing it. Run up and hide behind something, no point in shooting it out.
Maybe move A to the Allies side of the bridge and add something there worth fighting over? Trenches or defensive positions of some sort. That would force axis to get across the river and make it worth it for the allies to try and flank. Steeper banks would make the bridge more valuable and believable.
B is too narrow, as is this middle section of the map in general. It feels odd, to have a big wide approach with a single A cap and then it narrows down to a small courtyard. It'd be nice to be able to if not flank through the houses on the allies left of B, at least have openings in the debris blocking the streets for axis to shoot out of and allies to return fire. If you want to force all traffic through B like the gate to the city, maybe some enterable buildings where axis and allies can shoot into each others zones, but they can't enter.
B plays out similar to A except it's a nade fest. Run into the courtyard and hide behind cover, both Axis and Allies know exactly where each side is coming from, so get your back to a wall and shoot anyone who peeks out. If there was more room to maneuver, it'd be more tense with the fighting more fluid.
C seems fine. It'd be nice if the little nooks on the sides of the streets opened into the buildings on the sides, even just into a single room to fire out of. Now, you dash into these small dead ends that feel odd and don't provide much of an advantage to either side.
I've only had one match where the allies got past C, it usually stalls there. Axis mg's can sit on the allies left and mow down anyone who steps out trying to get towards the train cars. This allows the rest of the axis team to move up and sit in good spots to nail the stragglers. A bit more cover could help the allies survive an attempt to flank right or battle in the trains.
Right now you can flank all the way around via the harbor to behind the last axis spawn. I can't really comment on the last half, since I only made it there once on a less than half full server.
In general, I think if you could poke a few holes in the unenterable corridors, that would make each side less certain in where danger lies. I feel like now, since you are within impenetrable walls, you don't have to scan your periphery, which especially for the defenders allows you to keep 100% of your focus on the attackers exit points. It would make it feel like less of a grind if there's more options for both sides.