I think the new bladesinger quite likely needs better spellcasting to compete on an even footing with the eldrich knight. Instead of advancing at 1st, 3rd, 5th, 7th, and 9th, I'd probably make it 2nd, 3rd, 5th, 6th, 8th, 9th, and maybe 10th.
Or else it needs the Song of Celerity ability more...