Depends how much work you want to do.  If you have a post hole digger for the bobcat, I would dig on two sides of the post with the digger.  Cut the fence about halfway between posts in what ever length you want to handle, personally less then 35 feet length.  With a little wiggle fence should lift right out of ground.  Repeat without digging for those you don't need to pull out of the ground.

My personal prefrence would be to take them out of the ground by digging next to each post.  It really isn't that bad as far as labor.  Most work is backfilling the hole for them.