The usage of which vs that is a common grammatical confusion. A general rule of thumb to remember is :
'Which' is used to provide additional information about the subject but is not necessary ( in a way that it doesn't change the meaning of the sentence ).
For example :
'Our office, which has two lunchrooms, is located in Cincinnati'.
Here, 'which has two lunchrooms' provides an additional information about the office but it doesn't change the fact that it is located in Cincinnati.
Our office that has two lunchrooms is located in Cincinnati.
The usage of 'that' here is a must to point out that we are talking about one of our offices which has two lunchrooms. ( aka restrictive clause )
Another thing to note is :
That refers mostly to things, though a class or type of person is also sometimes referred to by this pronoun:
“He has the key that fits in this door.”
“This is a team that is going places.”
So technically, the first sentence seems to be more correct to me.