1) Price: For entry level models Fender cost an extra $50 compared to Ibanez, and that was just to slap on a sticker that said Squier; nowhere on it did it say Fender while my Ibby may be a Gio but it's still says Ibanez on the headstock.
2) Better Quality: I have the cheapest non-starter pack basses Squier and Ibanez make (Bronco Affinity and GSR200) and it's hard to compare the two. The Ibby keeps its tune better then the bronco, the bronco only has one pick up while my Ibby has three. The frets on my Squier had to be sanded down, and it doesn't even have a fret board. If someone was forced to gig with one of these basses, you could make do with the Ibby, the bronco not so much.
3) Style (but this might be too biased for you to use): On my Ibby I feel like I can pull off any style of music short of folk. My Bronco seems like a one trick pony, I can play around with my technique all I want, but its tone is not going to change unless I change the strings. I'm also not a fan of the Squier's body style (but this might be because I started on the Ibby). I'm only a hobbyist, so at most I drag my instruments from room to room, and I'm only comfortable using a gig bag with my Bronco because there's nothing to grab on to besides the neck. I also have audio processing delays so I get lot of the sound waves going through the body of the bass into my lap, the bronco hardly transmits these compared to my Ibby.