if you are sneaky, chose lily as sneak crits will do more dmg due to her comp. perk and she does a lot of dmg herself melee
In New Vegas I'd stick with Lily, since she's good with guns AND melee. Veronica proved herself a pretty strong meele combatant. She can handle herself with her Powerfist. And Cass is very good with guns.
Lily covers medium/close range and direct combat. Veronica only direct fist battles. Cass close to long distances, depending on the weapon she's packing. I'd stick with Lily
So it's just a matter of opinion. If you prefer a melee companion, choose Veronica or Lily. If you prefer firearmed companions, Cass or Lily. Or, if you like both, Lily.
Personally I can't stand Lily's heavy breathing. Veronica can get you in to the BoS bunker and save you a lot of trouble in the process, so it's definitely worth having her for that, otherwise it depends on your play style or personal preferences.
If you are going for a ranged class pick Cass for melee Veronica for sneak Lily
Secondly Why ask this HMMM!!!!
In FO:3, the best female companion is Star Paladin Cross. The other one just dies in seconds.
Only if you don't give her power armor....