Ships & Modules

I would suggest a Curse, the main difference between the two ships is that a Pilgrim can run camps much easier, but the range of neuts of the curse gives you a much bigger safety net when it comes to actually engaging, and it can end up getting you a lot more kills

But to solo in 0.0 with both of these ships takes a lot of experience compared to others

Both are able to Solo Gank in Null Sec. They just have 2 entirely different ways of going about it.

The Curse is Shield Nano Kiting fit with long range Medium Neutralizers. It uses a TD to cut turret boats range so they can not hit you and use there powerful Neuts to drain away the Cap that keeps weapons, MWD, Invulns and Points active You can then sit at 20km away from your immobilized prey while your Drones eat there drones and then them alive. Missile Ships are an issue though.

The Pilgrim uses a Cloak instead of speed an Align time to avoid enemies. It sneaks up till it is right next to the target and uncloaks. Locks them, Webs / Scrams / TD Tracking Script / Neuts them then orbits close with AB and lets it's drones eat the enemy. The Pilgram has a smaller target window though since it can not get under medium guns. It can escape a solo target by Neuting off the point as well as ECM Drones but the Dmg is not high enough if they can deal more back. The Pilgrim is much more risk adverse as you can make it appear on the field only when victory is a sure bet.

Having a friend in a Bomber for ether ship and using Target Range Sensor Damps to keep the Bomber from being threatened by Medium Guns and Drones will allow you to quickly burst down Battlecruisers.

There low DPS is there biggest weakness. Your prey might have backup on the way and multiple point combined with a low tank is your worst nightmare.

The pilgrim is the cloaky one with short ranged neuts and an armor tank. It's best used with an AB to duck under guns with it's TD (tracking speed script). Given it's slow and short range like that, it's best for ganking missioners/plexers/ratters in 1v1 scenarios. It is less capable in anything other than 1v1 however. It's basically a pure gank ship despite its low dps. This is the ship you are looking for I think.

The curse is a more generalized combat ship. It lacks the cloak (works well with t2 ordinary cloak though) but has range bonused neuts. The range bonus on them encourages kiting which in turn allows it to engage several targets at once safely. Not as easy to run camps in it but in combat it's abilities are matched by few others.