My experience with BD vs DVD is that there is a noticeable difference. The dynamic range on BD is hard to beat. DVD audio and video was incredible when it first entered the market but now it feels very dated. In my opinion of course.
That very much depends on the movie. Some of the newer soundtracks are mastered poorly or they tried to convert something to Atmos that was originally DD 5.1 and it doesn't really work.
I'd be willing to bet if you took what was considered a good DVD release and put it up to the same movie on BD, there wouldn't be that huge of a difference in sound. Video, yes, but not sound. Again, this greatly depends on the movie so it's not a rule or anything, but it's been true quite a lot.
Now, the OPs question was is streaming better or worse than the original disc? For BD movies I'd say the original will pretty much always be better. No automatic quality adjustments or anything of the sort happening and there is a LOT more audio data in BD discs than streaming movies.
Is it ALWAYS better? Probably not.