hmm the first one makes me think "It seems like it's going to rain" or "it's as if it were going to rain," whereas the other one is more like "looks like it's going to rain"
In this particular case, the former seems like hearsay, while the latter is the speaker's own judgment. Probably it's from the form of the verb 降る. 雨が降るそう(です) also expresses "hearsay."
A grammar book at hand says "yooda" expresses the speaker's conjecture based on judgment gained through the speaker's experience. "So" on the other hand is judgment based on the physical appearance.
雨がふりそうです。 Ｔｈｉｓ is a judgment based on how the sky looks like.
雨がふるようです。This is a judgment based on pieces of information that do not rely on how the sky looks like.
A simple google sampling as below shows 雨がふるようです appears to take place in forecasting or talking about how the weather going to be like based on what one has heard from news.
梅雨前線の関係からか、まだまだ強い雨が降るようです
土曜日は雨が降る ようです
明日は天気が良いみたいですが、明後日には、また雨が降るようです
「風吹けば雨」または「風が東から西に吹けば雨」ということわざは福島県その他の地方でいわれているように、この風が吹いた後は、雨が降るようです。