A nerd could be considered a compliment. A nerd is like a really smart person or someone who knows a lot about a particular subject (math nerd) but isn't necessarily negative.

A geek is more of an insult, IMO. It also refers to a smart person or a person who knows a lot about a particular subject (band geek) but it does so in a negative way.

Some may disagree with this analysis, but that's my take.

Seesaw