Pompey fan here.
I think for most of our fans, Plymouth have become our de facto rivals purely because we're the best teams left in this league after last year, and the last four games between us have been extremely eventful. After four years in League 2, clubs that we've never cared about before have become stereotypes (Newport are cloggers, Wycombe timewaste, Stanley are plucky, Orient are underachievers), and your stereotype is our rival who gets the better of us. If the last year was a Hollywood movie about Pompey, you'd be the main bad guys.
I must admit, when the fixtures were announced at the start of the year, I hoped we'd clinch promotion against you. More than anything, though, I'd be happy for us both to go up so we can continue the "rivalry" next year. Football's always more interesting when there's a few years of backstory.