彼はまじめそうな顔をしているが、本当は遊び過ぎ。
He looks like a serious person, but really he messes around too much.
彼は食べすぎたような顔をしている。
He looks like he ate too much.
How do we know when to use which if they both mean ‘looks like’?
I looked this up on Tae Kim and he says “The noun 「よう」（様） is the most generic word used to describe an appearance or manner of a state or action.” and that そう can be used for guessing from observation or expressing hearsay, but that doesn’t tell me which one Bunpro is looking for.
I will type the answer in 24 hours since it will be longer one 
So, first of all そう cannot be used with past tense and nouns.(unlike よう and みたい).
When そう follows verbs that depict some action(we are not talking here about hearsay そう!) it means that judging from what we see, something is about to happen.
So, 彼は食べすぎそうな顔をしている。would mean that
“he makes a face like he is about to eat too much.”
雨が降りそうだ。
It seems like it is going to rain/ it is about to rain.
彼はバナナの皮を踏んですべりそうだ。
He is about to step on banana and slip.
When it follows state of being verbs the meaning is similar to みたい/よう. (with differences described in my other post).
彼は素晴らしい車を持っていそうだ。
彼は素晴らしい車を持っているよう（みたい）だ。
In this case (I will be adding alternative answers to all those points this weekend).
彼はまじめなような 顔をしているが、本当は遊び好き。(should be 遊び好き btw!)
is also alright.
It is important to notice that Noun1のような(みたいな)Noun2
Noun1はNoun2のように(みたいに)Verb are used to say that something is similar to something else in appearance or in the manner of doing something.
And on this we focus here:
https://bunpro.jp/grammar_points/373
https://bunpro.jp/grammar_points/138
よう
https://bunpro.jp/grammar_points/107
みたい
Also, this is how it might be interpreted by Japanese speaker:
このケーキ、美味しそうだ。
This cake looks tasty.
You say this when you see the cake, and from it looks you guess it is tasty.
このケーキ、美味しいようだ。
This cake looks tasty.
You see a cake(since it is “here”), but you have some information like you heard from a friend it was good, read in book, heard in radio etc and based on that you guess it is tasty.
So for example, you can say the first one when you are about to eat a cake which can still turn out to be not as tasty as you thought, and second when you see your friend who ate that cake second ago and he enjoyed it and based on that you say this cake looks tasty.
If you want to point that based on looks it is tasty and really want to use よう/みたい you can use 見える to point that:
So, このケーキ、美味しいように（みたいに）見える。 means exactly the same thing as このケーキ、美味しそうだ。
Or just 美味しく見える。
Or
このケーキはおいしいような見かけをしている。(quite wordy)
But those three will look a bit unnatural(but there are some people speaking this way).
The ordinary Japanese person would just say 美味しそうに見える or 美味しそうだ。and we should follow that 
Is there a difference between 美味しそうに見える and 美味しいように見える? The last one is missing in the structure for にみえる.
Yes, most of Japanese would say 美味しそうに見える, and consider 美味しいように見える unnatural but understandable.
Cheers for the explanation.