Sentence Correction

Hello, folks....

Here is the passage that needs to be corrected:

Suppose you want to buy a coat. You have to choose between two coats. One of them has affordable price, looks great and of your style; however, the brand name is not very popular. The second one is more expensive, looks okay, but not as good; however, it is produced by Louis Vuitton, and is warmer.

Is the expression "not as good" would be correct in GMAT?
Shouldn't it be like "not as good as the first one", or we may omit "the first one" here?

Thanks in advance

Is the expression "not as good" would be correct in GMAT?
Shouldn't it be like "not as good as the first one", or we may omit "the first one" here

I am not very sure but I think we can omit "the first one" because we know the comparison is between the first one and the one we are talking about now.

I would wait for others view.
Thanks