I stayed in a palatial suite on the top floor of the Palmer house years ago. It is full of old-world charm. The Drake is very, very nice and in a much nicer neighborhood. Plenty of night life within walking distance.
The big-old Conrad Hilton on Michigan was one of the world's top hotels in it's day. These days it's in a dead neighborhood and a bit dumpy.
The Drake would be an easy choice for me.