I said same PATTERN, after I said same NOTES (ie we're talking about 2 different tunings). BEADGB is the same NOTES as a guitar, minus the high E and plus a low B. BEADF#B is the same PATTERN, as in, with the six strings, the interval between each string is identical to that of a guitar. So you can play your "open D chord" on a based tuned BEADF#B and it's still the same chord (just in the key of A instead, thought I had laid this out pretty clearly over my posts).
With the same NOTES, you can still play that chord, but you are missing the high E string, so you can't play the whole chord, just part of it (D, A, and D, so no F# which is the 3rd and could be important).
So again, it depends on which is more important to you.
A) Playing shapes identical to a guitar but in a different key (BEADF#B)
B) Playing only partial shapes identical to guitar (if the use the high E), but with full translatability of lines between guitar and bass (again, without the E).
C) Having the same interval between every string ("traditional" BEADGC)
Which one you choose will depend on your playing style, musical style, and just what you feel comfortable with, and of course there's no reason why you couldn't switch between them depending on the song/situation.
Also, "playing a chord doesn't have to mean strumming it like a folk guitarist. You could be arpeggiating it, tapping it in a latin jazz kind of way, or a bunch of other ways.