Are you wanting to fix the current cab with the piece you have? They both look like they are in pretty rough shape, might be better off using a new piece and maybe getting some side art printed up to try and match up.
No matter how you try to do it, short of replacing the whole side, it will show a seam of some kind unless you replace all the side art.
I guess you could try to make a nice smooth straight cut on old side and a new piece and put them together either will some dowells or bisquits.
But it will be really hard to get a nice seamless fit, especially with particle board.