Finally got a new mounted healer

You used the free summon on someone else then, sad but Veronica will still stick around so pray for her reappearance.
As for the staff, recover heals more hp overall, restore heals debuffs.
I personally think recover is better on Elise for more healing using her high attack.
On the contrary, restore would lower her healing but the effect would be minimal due to her naturally good attack stat.
It depends on whether you want a unit to be focused on healing, or to push her into a more supportive role. Both are great staffs to use.
I personally won’t do it because Elise has really low health and low bulk, in situations where she would be in an enemies range, I’d rather she heal more before she were to fall.