I had the same choices in front of me, a few years back.
I consulted some seniors and decided to opt for IIT BHU Pharma. After a year, I changed my branch. One of my friends who also had these choices decided to go for IIT Dhanbad. Even he changed his branch after a year. I changed my branch and opted for Mechanical.
I would say both choices are equally good. For CAT/UPSC prep, these two branches are easier and will allow you more time for studies. Even if you want another branch, study hard so you can switch.
I wouldn’t recommend a drop. Both the IITs are good, and a year of preparation will allow you to switch to another branch. This way you’ll always have something to fall back on. But if you are determined to score higher in the next attempt, you may consider taking a drop. It’s very difficult to remain positive and motivated in a drop year, and the decision is a bit risky.
Whether to join or drop is your personal decision. But I would recommend you join any of these two courses/colleges.