Let's look at how John Moore performed with Del Zotto and Klein as partners to see if he improved with Klein.
Possession
With Moore-Del Zotto the Rangers attempted 20.80 shots for per 20 minutes, and conceded 17.78 leading to an attempt differential of
+3.02 per 20 minutes ->
+9.06 per 60 minutes (entire game for context).
With Moore-Klein the Rangers attempted 19.47 shots for per 20 and conceded 19.67 shots against leading to a differential of
-0.22 per 20 minutes or
-0.66 60 minutes.
So we created less and conceded more with Moore-Klein. Zone starts and opponents aren't an argument for the difference as Klein actually received easier zone starts than Del Zotto and the same competition (he even faced lesser forwards). If we adjust the numbers for zone starts it comes out in an even bigger favor of Del Zotto.
I think their samples are way too small for a goal-based analysis, but some aren't sold on possession numbers so let's look at the actual results in terms of goals as those are the ones that win games.
Goals
With Moore-Del Zotto the Rangers scored 0.770 goals per 20 minutes and conceded 0.533 for a differential of
+0.237 per 20 minutes or
+0.711 per 60 minutes.
With Moore-Klein the Rangers scored 0.605 goals per 20 minutes and conceded 0.404 for a differential of
+.201 per 20 minutes or
+0.603 per 60 minutes.
So Moore-Klein is a lot closer to Moore-Del Zotto in this department, yet not completely there. Considering the difference in possession numbers, the goal differential of Moore-Klein is a lot less sustainable than the differential of Moore-Del Zotto.
Conclusion
Our third pairing got significantly worse after the trade and I'd take it back in a second if I could. Klein is not worth his contract on the Rangers and should be traded.