There are loads of good covers. Covers of Dylan songs are usually better because the guy can't sing. Mr Tambourine Man by The Byrds, a well known example. Loads of others.
Rod Stewart was usually very good at interpreting other people's songs. All three versions of The First Cut is The Deepest are great, but Rod's is the best. Handbags and Glad Rags, Sailing, You Put Something Better Inside Me. All great.
ELO's version of Roll Over Beethoven is better than Berry or Beatles.
Jealous Guy by Roxy Music, very nice musically, but not as personal as Lennon's.
Led Zeppelin ripped off all sorts. Whole Lotta Love is a classic, but is just a reworking of a Small Faces track, You Need Loving, which was itself a rip off of a Muddy Waters song.
I'll put in a quick vote for Whispering Grass by Windsor Davis and Don Estelle. Better than the original. 🙂