Not really.
Egis can be commanded in a variety of ways (through the pet hotbar), like staying at a specified location or focusing on a target while you focus on another.
And most importantly, they're "semi-independent" and stay as long as you want/need them to.
Demis on the other hand, are only available through a short burst window and can only attack (and even then, only the same target as you).
Plus, they have difficulty attacking while moving since they keep following you (unlike Egis).
So as you can see, it's not quite the same.