"That outfit is not thick."
I think ないです is much more common in spoken speech
Yes, you are right, but in Japanese there is something more to consider. If one is speaking to 'higher' persons (ages or social status), '～くありません' (or some even more polite forms, depending on the difference of status) is preferred. Some 'higher' people do not like to hear the polite form 'ないです' because it could be understood as 'ない' + 'です': one might say something boldly as to peers until the 'ない', and found it not very good for the conversation, and add 'です' ad hoc. However, if two speakers are equally levelled, 'ないです' is fine and more common.