I'd presume that by "drywall shims" you mean pieces of drywall to bring the surface out to the level of the plaster. In that case, your two options are essentially the same thing, and, I think, a great idea.
I'd suggest, though, that before you start down that path, you measure the thickness of the plaster & lath from the stud face. You may be better off using strips of plywood/OSB that are a very close equivalent to the thickness of what you've got there. There is a lot more variety in plywood/OSB than there are in drywall, so you could probably match thickness in one layer instead of having to build it up. Of course, if the thickness you need to build out exactly matches a sheet of drywall, then you've got all the options in the world!
Additional items of note:
That insulation has a vapor barrier on it, but it's useless, since it's not contiguous and it's not all oriented correctly. I hope that it's simply being used for sound deadening on an interior wall. If not, you've got a really cold wall and the next point is critical...
I'm assuming this is not a load bearing wall. If so, you've got a significant issue where the top plate is cut through for the pipe on the right-hand side.
The pipe on the left-hand side appears to completely bypass the top plate, meaning that your furring will have to leave a gap to accommodate it. You'll probably want to use some steel protector plates (usually used to protect electrical wiring in the wall) to protect the pipe so you don't accidentally try to run a screw through the cabinet and directly into your water supply line.
Do note JACK's recommendation to also do something about the cable conduit run, as well.
And now you know why the previous person left this part of the wall unfinished... It's unprofessional, it looks bad, and it's going to take work to do it right.