Both are correct. And they can be used in same context. The difference is in the hidden subject. "忙しいようです" have the mean that (I heard from somebody that he/she) looks busy, "忙しそうです" have the mean that (I found that he/she) looks busy. But as the difference is so small, they can be replaced each other in most contexts and make sence. 忙しいようです → 忙しい様です 様 means "state,situation" 忙しそう "like,looks like" そう means Sorry for my poor English.

施設や交通機関などを(お金を払う場合を含んで)使っている人のことです。 We call customer "客" and "利用"means "use". 利用客means a kind of customers in some places such as hotel,transport and ext. We don't use 利用客 for shoppers at the store.