Improved invisibility doees the same thing, except at level 4. You obviously cant trick the AI into thinking you left via dimension door, and when the AI uses it, you can see its shadow door and not dimension door anyway...

You can't put a level 4 spell in a level 5 slot, so if your level 4 slots are full (or, in the case of a sorcerer, used up), you can get the effect using a level 5 slot instead.

(This is the result of the game segregating magic resources by spell level, which is a mechanic that doesn't really make sense to me, and never has.)

In a nutshell, P&P role playing. However, Shadow Door does have a short casting time. Something to consider.