Lambert was in a worse situation. She was weak, unarmed and had no idea where the creature was or where it might come from. She had no truly well armed protectors. No group of marines, no dropships or promise of search party.
Its easy to be afraid under those circumstances.
Hudson had weapons, auto turrets, motion trackers, comrades, vehicles, and military training/experience. He even had the information from Ripley ahead of time, the physical strength of a grown man, a good synthetic, capable superior officer and a gameplan. And with all this he was still losing his sh!t.
Was it cowardice? Probably. But to be afraid with all that manpower and equipment on your side must've meant he was legitimately scared to death.
I couldn't decide between them.