My answer is only related to the BITS Pilani Goa campus as my knowledge is limited to the same. Here, the most relaxed and laid branch you will find is Mechanical.
The level of difficulty and workload of any branch depends on its lab sessions while the course difficulty is almost the same since BITS follows a relative grading system. Now, when it comes to mechanical, the lab sessions are pretty laid back. All you have to do is turn on the heater in the apparatus and just note down readings after every 10 minutes. Students spend this time gossiping and chilling around. Moreover, this is a group work and only one student is capable of doing such an easy task while others relax. Lab sessions of other branches are very hectic and often extended to 3-4 hours.
The Mechanical branch is good either way; if you are genuinely interested you will land a decent job in the core. If you are here just for chilling, you can relax and still get placed in some non-tech job.