no there different designs... the 1155 cpu wont fit in the 1156 socket and vise versa.
the only thing they have in common is the spacing for the hsf mount.
you have a 870 then theres no need to upgrade, the performance gains would be nominal for the money you would have to spend.. especially in gaming you would be lucky to get 2 extra fps on a cpu bound game.
out side of gaming you may get 7-10 percent gains at stock. so its not a huge leap... stick with what you have until haswell arrives, then you should hopefully see a 50%+(guess) improvment over the top of the line 1156 architecture.