Hello aspirant,

Hope you're doing well.

Both of them have their pros as well as cons. Not many good colleges provide the 4 year integrated course of BA and Bed. But, if you can get BA in a good college like that of DU colleges or any centralised university in India,  you should just go for it and apply for Bed. You may also get Bed from a reputed institution. However, at the same time, the 4 year integrated course can save you 1 year, which is a lot.

Hope my answer helps you.

All the best.