Hey guys, thanks for all the input. Yes - my Ibanez is active and does have roundwounds on it. I tried both Fender and Squier Precisions at the weekend. Great sound, but I just couldn't get along with the neck. Just too chunky, especially after the Ibanez. I'll try the Jazz again, and with flats 'cos I've never used them.
Yes - I don't really have the 'need' for another bass, but I could do with a back up, and I just fancied getting another one! I suppose I've come to the conclusion that the Ibanez does really do all the things that I want so I'll probably go for a Squier to keep costs down.
All other recommends welcome though!