IMO, there is no harm asking for formal offer letter (probably a soft copy).
But I would suggest choose the job which is of your interest. Salary should be the second factor. If you choose a job of your interest, you will perform well there and your career growth will be much faster there.
That's my opinion too. I worked in two different jobs in the last years. One of them was in company A, which I always wanted to be part of. The salary was not amazing (in fact, after of some talk with friends, it was low), but I was happy.
Then, I worked in company B. The salary was superb, it was higher than average, but I was not happy. That was not what I wanted. I quit.
But I would suggest choose the job which is of your interest. Salary should be the second factor. If you choose a job of your interest, you will perform well there and your career growth will be much faster there.