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If you've got a HE noble on an eagle w/ a lance which makes him more survivable in combat: A, the Golden Shield (shield that requires enemies to reroll hits in combat) + heavy armor or B, Dragon Armor (2+ save that can't be improved)?

Also how different would it be if he had a great weapon with the Golden Shield?

The Better option would be the Armor of Caledor (2+ can't be improved) w/ a Great Weapon. Since High Elves aren't hindered by Great Weapons, and mounted Great Weapons hit at +2S, that's your best option.

Since Great Weapons are two-handed weapons, the Golden Shield would not be used in Close Combat.

The golden shield is a good magic item at avoidance.
It turns a 1/2 chance of being hit from most foes to a 1/4, which is not bad at all.
It really excels when the opponents need a 5+ to hit your noble, which requires a WS of 2.
This changes the chances from being hit from 1/4 to 1/9 -- a huge advantage.

The shield also augments very well from magic modifiers -- speed of light from lore of light comes to mind. Raising the WS of the noble to a 10 means that a WS of 4 still only hits on 5s. If you add Pha's Protection, then the noble is only hit on 6's, and those hits are rerolled -- giving a 1/36 chance of being hit!!!

I use the sword of might and golden shield on a noble, and it brings her magic item allotment to 50 points.
Is it better than a 2+ armor save? Thats debatable. What it does allow you to do is to put that 2+ armor save on your BSB.

Golden Shield as stated halves the hit rate for most enemies dedicating attacks toward the bearer. On an Eagle w/ Heavy Armor and Shield, he's also only one point worse in armor save to my understanding. That sounds like it'd be best, as discounting 33-50% of incoming hits is always useful.

However, Dragon Armor is better against some other enemies. Anything that uses flaming attacks, to my understanding, is nerfed heavily against said Noble (to the point that a Flame Sword Herald should be unable to harm said Noble, to my understanding). A static 2+ is also better versus shooting than the (useless in this regard) re-roll in HtH.

Situational, really. Gunlines or things with nasty flaming attack units? Go Dragon Armor. Things that can hit 'ard in hand-to-hand with not-so-much shooting? Go the shield.

Dragon Armour+ Helm of Fortune+ Shield+mounted+ magic weapon + way to go with this nobel of yours