The fundamental difference between BE and BTech is the way these courses are delivered. Contrary to the popular misconception, BE isn’t just theory oriented. Both BE and BTech coursework includes theory as well as practicals. But a BTech offers a more in-depth and advanced level study of a particular field. While BE covers the fundaments. 

There are no such differences between BE and BTech, other than the course pattern. These two courses are considered equivalent. In terms of preference, your institute will matter more compared to your degree. IIT students certainly enjoy some advantages in terms of placements and higher studies.