The speaker makes a conjecture based on some reliable information(e.g., what s/he has seen or heard). らしい is more objective than ようだ, and the degree to which the speaker is dependent upon other sources is higher than that of ようだ.
*For non-past affirmative na-adjectives and nouns, drop the だ ending of the plain form.
中村さんは、しあいで友だちに勝ったらしいです。
It seems that Mr./Ms. Nakamura beat a friend in the game.
ラジオで聞きましたが、明日は天気がわるいらしいです。
From what I heard on the radio, it seems that the weather will be bad tomorrow.
あの仕事は、どうも大変らしいです。
That job seems to be tough.
明日は雨らしいです。
It seems it's going to rain tomorrow./I heard it will rain tomorrow.
Lesson 25-1「田中さんは留守のようです。
It seems that Mr./Ms. Tanaka is not in.
ようだ is used when the speaker makes a conjecture based on some information, but it gives an impression that what s/he says is also his/her own idea.