BITSAT

This is really a tough question because both of the question paper has its own perks and difficulty.
But according to me JEE is more difficult than BITSAT because JEE has questions asked based on the concepts of the syllabus and they do not directly ask any.
They are two different examinations based on very similar syllabus except for a few things.
I have written both the examination, so I know that major difference is not the fact that BITSAT include English and logical reasoning.
For JEE Mains, one is set 90 questions and given 180 minutes.
For BITSAT, it is 150 questions in 180 minutes.
Observation that comes from experience:
Time is crucial.
No doubt the overall difficulty of BITSAT is less.
Time is very crucial.
If one is concentrating only on JEE and solves BITSAT paper, you probably will fall short of time. The shift is about 120 seconds per questions to a question a minute.
So, actual absolute difficulty of questions: JEE>BITSAT.
Actually solving questions considering difficulty and time stress : JEE is nearly equivalent to BITSAT.
The BITSAT has a lure of 12 bonus questions- if you attempt all 150. Do not chase these questions by attempt and marking questions you don't know about.
Hope it helps.

Cracking BITSAT isn't about the books you use. It is more about clarity of concepts and lots of problem solving and an excellent time management. If you have prepared rigorously for JEE then you won't need any extra book for BITSAT. Rather I would suggest giving lots of mock tests. Make sure you are thorough with all the formulas and general solution for simple cases as it can save a lot of time in exam.
The main point is timed practice and lots of revision. Apart from that take a look at previous year's papers. There are some books available in market for mock tests but buy only from trusted publishers. Have confidence before going to exam or your entire preparation will be of no use in the end.

There is no coaching for BITSAT as such. You have to prepare for JEE properly and you can crack BITSAT.
Self-Study is the most important aspect which no one can deny, but coaching certainly gives an edge. Good coaching always give ample time to do self-study. Over the years the number of coaching for JEE has grown and each of them claims to be the best, so JEE aspirants seem to be confused of which coaching to take which will be best for them. I am putting forward the Best IIT JEE Coaching Classes in India:-
Allen Kota 2000+ students have cracked JEE Advanced and 25000+ students have cracked JEE Mains. The best part about Allen Coaching is that it gives individual attention and helps the students to excel in all the important entrances, so they do not only focus on JEE Advanced but also on mains, BITSAT and also board exams.
Vibrant Academy - 1400+ students have cracked JEE Advanced out of 2800 students (I.e. 50% success). The faculties in the top 3-5 batches are one of the best in India. But the important point here is that it is highly focused on JEE Advanced and do not give much time on other entrances and board exams.
FIITJEE South Delhi 2 in Top 100, 9 in Top 500 & 20 in Top 1000 All India Ranks secured by Classroom / Integrated School Program, 668 Students of FIITJEE South Delhi Centre from all Programs have qualified JEE Advanced, 2015.
Sri Chaitanya and Narayana (CHAINA) Hyderabad. They got Top 3 IIT Ranks in JEE Main 2016. Madhapur campus would be better if u are willing to stay in the hostel. Classes begin at 6am in the morning and continue till 1pm, then you have study hours from 2pm and continue till 8pm.
Resonance Kota- 3500+ students of Resonance cracked JEE Advanced (note: it is from all over India centers). The faculties in top 2-3 batches are experienced and are well capable to guide you to crack JEE, but the lower batches do not get great faculties.
There are other coachings as well like Vidyamandir Classes New Delhi, Super 30 Patna, IITians PACE Mumbai, Aakash Institute New Delhi, etc. I have written vividly about all the good coaching in my blog Top 10 IIT Coaching in India.