Daf

The top original handle in your  first photo the plastic clip that holds the rod on is from a xf (rod has a90degreee bend in it. Xd/Xe rod had a S shape bend in it and goes through the eyelet grommet that came that came on the new one. I would say the hole drilled in the new arm is to large for the xf attachment. You could always make up anew rod but I would just repair you old one

Yeah, they're usually a bit sloppy. The originals were obviously better. Maybe fix it with a washer and a self tapper.  The rod that fits in the plastic holder (on the right), can be adjusted, by spinning it. Have a look inside the door, you'll see the thread on the other end of the rod.

it will work, they usually have that much slop in the mech anyway. 
 
but yeah, fix the original and it will probably outlast the car. especially if the hinges aren't worn and the door is adjusted to the striker well

Really?  I could've sworn they were on the old FC I owned. Oh well, there ya go..... my bad.
Sorry Daf, I do drink a lot......

i don't think the XD- XF are adjustable but you can bend the rod to take up some slack also.. (or straighten it if it's too tight)
 

I've drilled out the original, stuck a 4mm bolt thru and fixed the original. Good as gold.
 
The plastic retainer clips are also different so when I did fit the new one in and lifted the rod up (yes there is some slack) it just popped straight out under pressure as there was 'nothing' holding it in place. 
 
The guy at Rare spares also told me that the rod would be "adjustable", however it's not.  Inside the door the rod goes down and simply hooks onto another lever on the inside of the lock mechanism, nothing adjustable in there.
 
Are all doors across the model range the same??  Maybe GL door handles are different to ESP to Fairlanes??