Ideally, most of the above Universities have similar number of seats in Engineering, only fact that BITS Pilani has 3 Campuses, Pilani, Goa and Hyderabad hence more number of Seats.

As far as chances in admission are concerned, BITS Admissions are totally based on merit, and you need to secure a good Score in BITSAT (300+ Minimum)to stand a chance in securing Electrical/Electronics at one of the 3 BITS Campuses, with Pilani Campus Cutoff being anywhere above 330-340+ for Electrical.

As far as Other Institutes are Concerned, I believe VIT Vellore has a much relaxed admission criteria with the Category system. You may take admission in EE, from a lower Category, by paying a Net Higher Tuition Fees, in case Higher Category Seats are Filled on Merit in VITEEE/JEE Main as in this year 2021.

On the Other Hand Manipal has a much structured admission and counselling system, and you do have a great chance in securing EEE at MIT Manipal provided you are seriously preparing for Engineering Entrance Exams. MIT Manipal also has great Placements, being located near Electronics and IT Hubs of Bangalore.

My preference Order, If I were in your place would be

1. BITS P/G/H

2. MIT Manipal

3. VIT Vellore

4. VIT Chennai

5. SRM Chennai

All the Best !