This is definitely a movie that was on high rotation for me as a child as well. I really like "Portobello Road," "Age of Not Believing," and "Bobbing Along." I agree, I'm not sure how well this holds up without the nostalgia factor, though. I showed this to my kids a few years ago and they really couldn't be bothered.
It's also funny to me how much I loved the animated sequence as a child, but now I think it's the weakest moment.
Since I think the comparisons are inevitable, I think Mary Poppins has the better music, and is better done overall, but I think I prefer the story of Bedknobs and Broomsticks -- even if I'm a little disappointed she gives up being a witch at the end.