Both are correct. 忙しいそうです。 You think they are busy because you hear it from someone 忙しそうです。You think they are busy because you can see them so/ they look like to you so. 忙しいようです。 　You think they are busy because you, considering the situation, guess so. 忙しようです。: NG, ungrammatical. 昨日Aさんからメール来ました。今、忙しいそうです。 おまえ、汗だくじゃん。忙しそうだな。 あいつが何の連絡もなく欠席するなんてめずらしい。 どうやら忙しいようだな。

Thank you Yu SZ.

忙しそうです means that he/she seems to be busy, while 忙しいようです ,means that I've heard that he is very busy.

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.