My impression is that AA and UA have more overlap than either does with DL because they share some hubs: ORD and LAX, plus have AA and UA have DFW and IAH respectively which are close to each other (and both have lots of flights to "smaller" airports in Texas, which DL doesn't have so much). However, you might want to make an extensive list of likely routes for you and compare the choices of connections and timings.

You're going to be connecting on almost all trips, unless your destination is a hub served from Manchester. Part of your choice should be which hubs have the best (mainline) service from your home airport and which offer the easiest and most efficient connections without many delays, cancellations, and missed flights.

From BOS, at least US/AA and DL (I'm not sure about UA currently with US no longer being a partner, but perhaps LH serves BOS from its German hubs at FRA and possible MUC) have TATL nonstops to partner hubs with good onward connections, although most FFers have strong preferences about where they want to connect.