You can apply to both, and they will be considered as 2 different applications.
If you put either Newcastle will randomly assign you to either, so dont think it will improve chances!!
The which is better question is rather subjective

For example Newcastle is Newcastle.. got the night life, get to know the place from the start and will understand Newcastle uni's ways... drawbacks - larger groups for everything (PPD, MIC etc), larger year group (not as personal? again subjective) etc
Queens campus - smaller year group, great very helpful staff who stay there the whole year, part of Durham University for 2 years and get to experience 2 uni's as a result, college system adds some fun to the mix... however your in Stockton not Durham
So.. its personal opinion
