XIII or 13 NZEF Reinforcement Badges which one is correct?

[xrayrifle]

Greetings from my perplexed mind.

I have been working on shadow box displays honouring the service of five of my great Uncles during the Great Great War.

Over twenty years of collecting all of the artifacts I now have what was originally planned to include and to make the shadow box displays now finaly possible.

Along the way, I have picked up two quite different Thirteenth Reinforcement badges.
Before I place the artifacts I think it would be wise of me to ask knowledgeable people which one of these two badges would be applicable to my great uncle?
He signed up and became part of B Coy Wellington Infantry Regiment and on arrival at Sling Camp was reasigned to the, 2nd Battalion Canterbury Infantry Regiment and then on to Messines and his death.

Any intel regading these two Reinforcement badges would be much appreciated.
Cheers
Bruce