I've come across sentences in KO2001 using both だろう and ようだ and am wondering what the difference is? Do they both mean: it appears as though..., its like..., it seems to be... etc.. the same as みたい?

Also can I use でしょう、　ようです。 as polite equivalents?

Any help on this topic would be appreciated!

The way I learned it: だろう/でしょう indicates uncertainty about something. The canonical example is the 天気予報: 明日は雨でしょう。

～ようだ/～ようです is very much like みたい, meaning that something seems that way. I'm not good with the subtleties there though.

だろう/でしょう is suggestive and leading. It suggests that something is or will be, but it is the speakers speculation. There is an air of pondering about it.

みたい/ようだ is a strong assertion of ones own conclusion that is based on what one has seen, read or heard. In other words it is strongly linked to evidence and the speakers experience which leads them to this conclusion.

Here are two example sentences about someone. Both suggest he (or she) is working.

1. 働いているでしょう。
2. 働いているようです。

For 1 it sounds like the person puts together the facts "He has a full time office job." "It is during normal office hours" therefore he is probably working. However it is speculation. He may be sick at home for example.

For 2 the speaker may know the same facts as 1, but there is some specific evidence that suggests he is working now. For example, maybe they saw him walking to work in a suit. Or his cell phone is off which he does when he works. This statement is more certain.

EDIT:

Yes those are the polite equivalents. However, note that だろう is very casual (depending on your location) and used primarily by men with their close (usually male) friends.

Also, ようです is very formal and actually humbles oneself a bit. If you just meet someone, but they are on similar level of station, みたいです is appropriate.

Think みたい is more a conversational thing.

Tae Kim's Grammar guide is pretty good on this http://www.guidetojapanese.org/similar.html

Thank you very much for your replies everyone especially thermal!
I think I understand what the difference is now!

皆さん、有難う御座居ました。