To be fair, Detect Magic isn't a replacement for See Invisibility. It takes several rounds and standard actions. On round 1 you just know there is magic in the cone you're projecting. On round 2 you know there is one faint aura. On round 3 you know there is an illusion effect and what square it is in, but don't know what specific spell. That should be plenty of time for an invisible opponent to get out of your 60ft cone.
Actually Detect magic should detect its own area, since it is a magical effect present in its area. So round 1 it detects the presence of magic, and round 2 it detects two faint auras. Round 3 it can find the school of anything that is in line of sight, but is an invisible creature actually in line of sight ? So it detects a faint divination aura, and another faint aura that may or may not be identified as illusion.
I'm not sure how the spell works.