Yeah I can see where you're coming from. The chords aren't really the same. I think the original chords for Dont Stop Believin are E B C#min7 and A. You could transpose it to be in the original key of Hometown Glory, B flat Minor. The way the chords are broken is roughly close to the same pattern in Hometown Glory. As for the rhythm, maybe that's what you were thinking is that they are almost the same type of broken chords, but they are both also in 4/4 time signature(most songs are anyways, but just pointing it out). That's cool that you realised that!
I'm trying to arrange a mashup of Halo by Beyonce and One and Only by Adele on piano, so I'm sort of doing the same thing right now. Not sure how I would make a Don't Stop Believin/Hometown Glory tho, after all the meanings of those songs are both very different despite all the similarities. Could possibly make it work tho :)