I'm not sure what "better frequency over the full spectrum" is supposed to mean, and the benefits of balanced are by no means as cut-and-dried as some might have you believe.
Professional gear uses balanced because, in the main, it helps with earth loops and noise rejection and long cable runs in electromagnetically noisy environments, and because it's robust. It's not primarily about sound quality in professional gear.
There are some technical limitations with balanced, such as the way that the phase inversion isn't perfect in the ultrasonic region which is said to affect frequencies lower down in the audible range. There are also some practical ones such as the quality of the circuits involved. In some gear they're not great and can degrade the sound for the sake of fashion.
Because of the way the summing of the two signal channels works, balanced produces a louder signal, and it's easy to interpret that as better.
The bottom line is that the results of balanced versus unbalanced depend on a number of factors. A well-designed single-ended connection using properly shielded cables may well be the better choice, particularly where the two bits of gear are essentially unbalanced circuit designs with a bit of bolt-on circuitry to add balanced connections because it looks a bit premium. You've got to suck it and see. Listen for yourself, just remember to adjust for the volume difference if present so that you're making a proper comparison.
