Ok, I believe that Fretful means "well known" rather than "reputable."
Yes, Ibanez is better known than Spector, but only because Ibanez floods the market with inexpensive models and buys endorsers left and right. They know how to market their instruments, and it has payed off.
Spector, on the other hand, is probably better respected than Ibanez. They are known for making VERY nice high-end models, and very good budget instruments. They make mainly basses (they do make guitars, but those aren't very popular) so their name isn't as out there as much as Ibanez, but they have been around since at least the early 80's and have their share of professional users.
As far as which of those two basses is better, the fact is that they are probably built in the same factory. Spector uses EMG electronics and pickups, whereas Ibanez makes most of their own in-house, except for low-end Barts on some of their models. It's really a matter of which one you like better, because quality-wise, they will be essentially identical.