As far as I can tell, the materials and weight are two distinct differences. The BBS is machined from 6262T aluminum and it specifically calls that out on Orvis' website. Looking at the Orvis catalogue I have, the Battenkill is cast, not machined. The drag system is likely upgraded in the BBS as well, but I would expect them to be fairly similar.
To answer your questions:
Yes, the BBS is the better made overall reel, made with superior materials. With that said, the Battenkill obviously has something going for it since it's been around so long. Opinions vary as far as trout reels. Many feel it's nothing more than a spool to hold line, my opinion is different.
Personally, I am a huge fan of the Battenkill Mid Arbor, the drag on that reel is unreal for the price and it's a fully machined reel. They're also on sale.