I'm putting aside the 'should they' part of the remake since that was not the OP's hypothetical. In this scenario, it's being remade period, and what should they do?
Well, the one thing that really strikes me about BSG is for some of its problems (overall story consistency, plotting, ironicallly B5's strongest asset), it really excels in a serious feel, which if you read JMS' original postings about B5 and how it was supposed to be like the Hill Street Blues of the sci-fi genre, to take a serious drama style look at sci-fi... BSG really did accomplish that. It doesn't have the "novel" feel of B5 but I think its the one shows critical community has rallied around as the 'Hill Street Blues' type serious sci-fi.
So with that in mind, yes a big part of that was stylisticly, while I would tone down the shaky-cam, I'd have a similar cinematic style.
The acting is one area where a redone B5 could be improved dramatically. There are many bad actors (Conway, Ivanova), a few actors who are average but are still likeable out of shear earnestness (imo Boxleitner, Mira, Jerry Doyle, Katsulas), and one or two good ones. On BSG the only actor I think was bad/mediocre was Cally, with Helo and Tori being kind of mediocre and everyone else imo was rather strong.
I think probably the Shadows could be more of a mystery in the vein of LOST or BSG's (non-existent) Cylon motives. Clark's totalitarian rule would probably be a lot darker. We'd have less standalone episodes. The music would be a little different style. Naturally the effects would be better. However, the overall plot shouldn't stray too much from the B5 we had.