Daemon Prince Vs anything else IMO:
Ppl said that ICs can hide in squads, but you can hide your prince behind a LR for example.
The lords have obviously one gear a prince cannot compete with, and thats the daemonweapon. +D6 attacks, with IK or poison 4+, or 2D6 attacks. Not bad, for particular roles.
A Slaanesh lord can cut through multiwound units, like oliterators, ork nobs and not EW characters.
A Khorne lord can have ridicuos ammount of attacks with PW
A Nurgle lord can easily kill nidzillas and other high T models (Mephiston eg.)
A Tzeench lord can shoot D6 Ap3 from a rhino for example.
The Sorceres are pretty much the same as a Prince, but: they can have a familiar, allowing an extra spell to make your HQ a bit more all rounded.
And they have force weapons, so can IK annoying characters, what a prince can't do. (not with a single hit at least)
And finally, all of them can have personal icons, and can be sacrificed for a greater daemon. A prince cant do either.
The named characters are another issue, they all have their personal toys wich you may consider worthy or you may not.
Don't get me wrong, i use 2 Princes in every list i write, but those are the reasons on the others side.