National Institute of Design, Ahmedabad

Can't be said which is tougher to crack amongst the two but yes, NID is considered the toughest among all design entrance exam as the paper is almost unpredictable.

Crescent classes are there for NID coaching.

Hi Samoyed,
There are no maths and science questions in NID entrance exam. They conduct a design aptitude test (that) which is meant to judge your creativity. This test is followed by a studio test. Please refer to this link for a detailed information https://www.shiksha.com/design/communication-desi

You should opt for NID if you want to pursue car designing.

Hi Ayushi,
You can choose NIFT because after graduating from NIFT, you can become a good fashion designer and can get good placements for what you required that is apparel designing.

No, it is not a compulsion to stay in hostel there.

No, there are only 8 designing branches which include:
1) Animation film design
2) Furniture design
3) Graphic design
4) Product design
5) Textile design
6) Film and video communication
7) Ceramic and glass design
8) Exhibition design

NID is the best institute in India for design courses.
For the that (Design Aptitude Test), there isn't much that you can do. Firstly and most importantly, you should have an aptitude for design. NID papers are designed in such a way that only those who have a creative side will be able to clear it.