I'm on the fence...
As a rule I'm not really a Fender fan but have heard good things about the Aerodyne, and I do like a PJ. Even though I own a BB615 I'm not really a big fan of the BB shape and will probably move it on at some point.
If I was in your position and had to keep one/ sell the other.....I'd probably start a poll and ask everybody else....
Oh yeah...you did.
If you happy to accept a well padded gig bag I would second (third?) Protection Racket. I've got a couple and they are very good. I'd also recommend Body Glove - I have one which I generally use when I'm taking a bass out of my home.
If you insist on a hard case - go Hiscox.
I've had several Bassballs - for me, they do everything I've wanted them to. I've sold them because, though I like to play with them at home, I don't think I'd use one in the real world.
Today there are loads of good basses for £500. I'm a big fan of the Bass Collection Nanyo SGC range - search around and you can find one for around £150 - you'll get loads of bass for your buck. There's a whole thread here where you'll find out why you should.
You'll also find G&L basses in that price bracket. I'm a big fan of the SB2 - and you'll find them available for around £300.
Lots of Squiers in your budget - I really rate the Standard model (PJ) - again you'll find these for around £200.
Sires - there is good reason why everybody has owned one - amazing basses for under £200.
If you can find a NS Spector for around £300-350 snap it up.
All the above basses are miles ahead of basses that were available when I started playing back in the 80s.
I also have "Dubber side of the Moon" by ESAS - the remix of the first dub album.
If you're a fan of Aswad don't forget "A New Chapter in Dub". Lots of recommendations above for Scientist, Chemist and The Mad Professor...pretty much your starting point I would say.
One of the best small bodied basses has to be the Bass Collection SGC Nanyos.
Like Ricky, I prefer the TRB and BBG5s bodies to the BB range, which others rave about.