What would be different between two years of graduate admissions? A bit of background to contextualize:

So I'm in a bit of a two-body problem with both me and my wife interested in applying for programs in the near future. Mine would be five-year-plus program and hers on the order of a year and a half.

If we were to apply for programs near to each other (but not near to our current location), and she didn't get into hers and I chose to decline that program, what sort of variables could change between years that might affect my chances to be admitted a second time?

I'm curious mostly about what would change on the department's end. This program would be in a funded, psychology-related program.
In the US, if you get admitted to a funded PhD program, often they will let you defer a year. If for some reason they are unable to let you defer, then the next year your application would be looked at fairly. A lot can change in a year, so it is no guarantee that you would get in again. The quality of the competition can change, the allocation of students to supervisors, and the amount of funding can all influence chances of admission. Sometimes faculty leave and the admission committee changes from year to year. Admissions can come down to a single vocal advocate.

If you get accepted to multiple programs and decline the offers (you can only really defer from one place), your application may not be judged fairly the next year. Admissions involve some politics and trying to judge if a student would accept is part of that game.