Is the (Shadow)Priest the better Mage in WOW?

[Drasca]

Simple question, but probably not so simple answer:

Is the (Shadow)Priest the better Mage in WOW for Solo-Play? Is there any argument - besides the DPS output -  that could convince me to play a Mage instead of a Priest with his self-healing ability and buffs?
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Some mage perks:
Crowd control (Poly a large variety) vs shackle undead (MC less effective solo)
Escape abilities -- many many more options than Priest, which is mainly bubble of love, scream, flay.
Portals to major cities + Blink
Instant AoE, extremely important

If you want to fight end-game, play a mage. If you want to heal, play a priest. If you want to be a masochist, play a warlock.