I'd have to put my money on the elder. Although the queen may have a massive size & power advantage, the elder's hunting experience over the centuries would be an invaluable asset in a fight against the alien matriach. All it would take would be one slip up for the elder though, & he would be skewered like a rag-doll. Although, if the elder managed to get in close & underneath the queen's defences, then a solid stab directly through the head with the combistick would more than likely do her in (in AVP when scar stabbed the queen, he got her through the base of the crown, I mean a stab to her actual head).
As for the elder's other, long ranged weapons, I doubt he would resort to using them, as it would take the challenge out of the confrontation.