Historically, Tear -> Archangel's Staff has been a scaling build at the cost of a delayed power spike. It was always extremely slot efficient, especially paired with RoA or other mana items. Changing the AP gain to 1% per 100 mana is not consistent with this vision. This is not the late game fantasy one wants when buying this item. A 1% value on this passive is negligible and makes one wonder why this passive even exists at all. It might even become a noob trap because players will buy more mana items due to the synergy but the reward would become totally unjustified.
A better nerf which doesn't bite at its very identity is to just raise the cost to match Luden's. Combined with the previous nerf, I doubt it would need more than this because delaying early power tends to have ripple effects throughout the game. Taking this approach would also make picking between the two items more a matter of just exactly what you want and not whether Archangel's is 100g cheaper. If it still seems insufficient, a 200g price increase would definitely do it. This would position Luden's much more as an early game item for a fast power spike.
BTW: If Seraph's appears too strong, it may also be that Luden's is too weak. Perhaps its proc. should have better scaling. 10% AP is incredibly low.