Can I swap the battery in my mbp 2011 with my 2010?

I have a macbook pro 13" mid 2010 edition, and a lesser used macbook pro early 2011 edition in my house (also 13"). I would like to know if I could take the battery from the 2011 macbook pro, and swap it for the one in my mid 2010 model. I would like to do this only if it is compatible with both computers and it won't hurt them. I'm thinking it would probably work since it's the same size computer as well as battery device name (bq20z451) however there are some slight differences I noticed while looking at the information for both batteries. The amperage and voltage in the newer macbook pro is higher, and the Hardware Revision is different than my mid 2010 macbook pro. Thanks for the help :)