I'm not sure getting both of them is an option, but I'll give you some reasons why I want each system individually. Note, I already have a PS3 and PS4, so I won't be missing out on any modern games either way.
The reason I want a PS2 is for the classics, such as DMC series, MG series, Kingdom Hearts series, Spider-Man series, Final Fantasy Series, X-Men Games, Jak & Dexter and Sly Series.
All of those have classics on the PS3, and the spider-man and x-men games are backwards compatible on 360, so... get a 360!
They cycle out, just update online again and maybe a lower level one will come. Also, they don't do anything, there's no negative benefit to having them around, just the xp/jp/pg from fighting them as a reward.
The lesson we're taught as kids that reacting badly to being bullied is worse than actually being bullied is one of the most damaging psychological things we do to our kids, and is probably the root of a bunch of my mental health problems as an adult.
So whilst the instinct is totally "you should be the bigger person" it's important to realise that's only because we were told that when we were young, and it is not a value that is beyond questioning.
If you've never played Persona, make sure to get P3P for PSP as well! Disgaea also has a PSV game that I'm told is very good? There's lots of RPGs that have come over from the PSP on the store, too, so that's where I'd look to pick some up.