Any graduate is eligible to pursue an MBA. So, both BBA and B.Tech make you eligible to apply. And if you pursue a BBA, you could even save an year, since it is only for three years. So, with a cursory glance it does appear that a BBA might be better option. But the catch here is the admission in good institutions.

Most Tier-1 colleges have a sizeable section of engineers in their batches. Our interactions with managment faculty informs us that, managment schools prefer a BE/ B.Tech primarily because they are exposed to a certain level of complexity of systems during their courses and hence are good at logical reasoning, analytical abilities etc.

More over  a good BE might also land you a campus placement, which is very rare for a BBA. Working for a few years before you apply for CAT/MAT increases your chances substantially to get into a good programme in a good school. The only catch here is the cost. But unless you get into a Govt college, the cost of pursuing a BE or BBA might be quite similar. So we would suggest for a BE.