I am considering using white acrylic eggshell for interior doors and
staircase.
Are there any advantages or disadvantages over an oil based eggshell
paint?

Advantages (of water based acrylic):

Easier to paint (opinions do vary, however)
Environmentally friendlier
Does not yellow with age
Does not stink
Fewer nasty chemicals

Disadvantages:

Less hard wearing
Less easy to clean

I always use water based acrylic myself, as the environmental aspect is of
high importance to me.

Christian.