Well, with the latest non SVN version lichdom has some nasty consequences on the long run. You end up being really undead, unless you worship certain daedra and are willing to pay ludicrous amounts of piety. So basically immortality spell let's you play an immortal character without any major drawbacks (except, maybe, for the lack of fertility) while lichdom turns you into an undead monster hated by everyone. Lichdom also has an impact on your skills, giving a huge bonus to learning (+5) and receiving a big penalty to diplomacy (-3 or something like that, plus any other after becoming completely undead).
But, hey, isn't it cool to be an undead wizard hated by everyone trying to conquer Tamriel with the help of his summoned undead courtiers and his wretched armies?