I hear jabs is better than Eviscerate. Because of that vampire has no benefit for you unless you want to drop jabs completely and go full vampire.

And by full vampire I mean go stages 3-4, use Arterial Burst + Sated Fury (Or Blood for Blood if you have the Pale Order Ring), build into spell damage like a mad man, slot Swarming Scion, and slot offensive skills that heal you since Vampiric Drain is worthless.

Also all effective vampire builds are required to have a source of major Sorcery (thankfully Templars can also have minor Sorcery to.) since the buff increases the spell damage from Strike from the Shadows and Sated Fury. Never go Simmering Frenzy unless you're a Nightblade bomber, because unless you enjoy dying a lot it'll be frustrating to use. Sated Fury at least gives some HP back when you turn it off, but in heavy Cyrodiil fights it might just be better to not use Sated Fury at all. It's a skill to use when you're ahead and winning, not one to use when you're on the defensive.

Mistform and Swarming Scion are probably the best things for PVP that vampire has tbh. Swarming Scion is a full heal and mistform will let you navigate the battlefield and dodge ball groups charging at you spamming stuns + AoEs. Mistform was buffed in Greymoor and it's really good, but the rest of the skill line is questionable. It only really works when you have the self healing to fuel it, which is why the Pale Order Ring imo is required for a vampire PVP build using Blood for Blood since it let's you cast that skill for free. Great sustain boost overall with that combo, but without the combo vampire is a sustain nerf.