Basically, みたいです is your assumption/judgement. It may be from your feeling, observation, what you heard, or information you got. Also, みたいです is used only in non-formal speech, not in writing and formal speech. (Formal equivalent is ようです) そうだ is your instant impression from what you see, hear, smell, touch, or taste. It's less logical than みたいです. In some situations, both may be possible. Example) You are talking about flu shot with your friend. You have heard some people say it' s very painful, and that rumor made you assume so. Then you'd say 「痛いみたいです。」 You are watching someone take a flu shot. His facial expression tells how painful the shot it. Then you'd say 「痛そうです」. Grammar note: There are other usages of そうです. One of them is hearsay (from confirmed sourse). But in this case, you put そうですafter a complete sentence with verb, adj, or noun+copula, whereas you need to conjugate the adj for そうです as impression. 痛いそうです（They say it is painful.） 痛くないそうです。(They say it's not painful.) 痛そうです。(It looks painful) 痛くなさそうです。(It looks unpainful.)

It is difficul to japanese too. 日本語ですが検索したら、 似たようなことが書いてあったので、よかったら読んでみてはいかがでしょうか↓(in japanese) http://soudan1.biglobe.ne.jp/qa5665013.html 丁寧さ（Politeness）：　そう＞みたい 確信性（Confidence）：　みたい＞そう な気がしますが私も間違っているかもしれません。 そうは見た感じそう感じたというときに使ったりも・・＞いたそう、高そう みたいは聞いたり実感したりでいうことも・・＞隣の奥さんは美人みたいね。

。。。みたいです。expresses YOUR opinion. 。。。そうです。conveys ANOTHER'S opinion.