Except for trains #66/67 (the overnight trains), there is no checked baggage service on any train between WAS and BOS. Except the trains to/from FL, NOLA and CHI - but you can not travel locally between WAS and NYP on them. So you must carry on the bags.

The regionals have plenty of luggage space. I am not familiar with the luggage storage on the AE, having ridden it only once (without luggage) for less than 1 hour.