Egg, mayhaps I was not clear above... Given a choice between a regular morningstar and a Valyrian Steel blade, which would a knight of Westeros choose? The Valyrian every time.
Valyrian steel has two amazing properties in my opnion. First, it is very lightweight yet very strong. Jon and Brienne both marvel at how fast their cuts and parries seem to be with a Valyrian steel sword compared to the regular steel swords they've been used to. The light weight makes the wielder into a faster swordsman than he was previously... plus I think there is an added benefit of a psychological advantage added in. The wielder thinks I'm faster now, so I'm better.
Second, Valyrian steel can be sharpened to an unbelievable and an unequaled extent. This edge allows the wielder to cut into regular steel. It makes a perfectly full plated knight with a shield seem suddenly vulnerable. Jaime remembered Ser Barristan's duel with Simon Toyne, the Smiling Knight... Toyne had to stop and get a new sword because after so much hard fighting his own had become blunted. I get the feeling that never happens with Valyrian steel. The added psychological detriment is imposed upon the opponent... Oh no, that thing will cut my wooden shield to ribbons! I need help or I need to run away... NOW!
The total psychological benefit is... I'm faster than I ever was! I have a weapon that will cause fear in my opponent! I'm unbeatable!
I can see how the weight of Valyrian steel could make a morningstar faster. I can see how armor could be improved also because of the light weight. But both would be missing out on the second key aspect of Valyrian steel... the blade's edge.
Yes, we do hear of an axe and at least one dagger made from Valyrian steel. The axe most certainly benefits from both the weight and the edge. I don't know that daggers suffer from weight issues, but putting that edge on a weapon made for stabbing would certainly help.
Now Egg, you make good arguments for Jeor's giving Longclaw to Jon over Maege. I can buy his shift in thinking, priorities, and allegiance from that of a minor baronial family to that of the military order for the salvation of the world. I agree that is what GRRM intends for us to see (and I agree with it on the surface and I'll probably make your arguments for you in the following sentences), but I'm playing the devil's advocate somewhat by wondering how the patriarch of a landed medieval family, a man of minor peerage, could just give away his familiy's most valuable heirloom. Not even the Lannisters had a Valyrian Steel blade, but the Mormonts somehow did. That symbol of power, nobility, and honor is not something to be lightly dismissed or tossed aside.
In bestowing Longclaw upon Jon Snow, his steward, his squire, and his body servant, the Old Bear must have finally (if not previously) taken the psychological step that the work of the Night's Watch superceded even that of his own family. I know that the NW takes vows of renunciation of family and bonds of loyalty from their previous lives, but merely obeying the rules and believing them in the core of one's soul are two different things.
I seem to recall that Mormont once said to Jon something like, "Your father sent you to us." The Old Bear seemed to view Jon as this generational gift of the Starks to the NW. Benjen had been the last generation's gift. Ben was intelligent, well trained, capable as a leader, and had influence with the Starks. So Mormont wanted that to continue through Jon.
Edit: Hope your flight is a safe one, Egg. Godspeed.