I have never grown brambles from cuttings, interesting. I threw out maybe 8 tip rooted plants this fall. They want to spread everywhere.
I always have liked unusual plants and I have 2 different white blackberry cultivars, and a yellow black raspberry. The whites though are known to be virus carriers and so I really don't trade any of my brambles out. I don't want to infect your garden.
For blackberries I have
Lochness
Columbia Star
Burbanks White
Nettleton's Creamy White
Triple Crown
Anastasia wyeberry
Boysenberry
Tayberry
Navaho
Chester
Black Diamond
Natchez
Siskiyou
New Berry
Marionberry
And a couple others I recently obtained, i forget what they are?
And out of these Marion is by far better. I think it is a lot better than Triple Crown myself. I also like tayberry a lot, it tastes more like a raspberry, it is tart, but the jam is so awesome. I also like New Berry a lot and Boysen and wyeberry both raspberry-blackberry hybrids. Natchez produces extremely large berries, but flavor is just ok not great.
Here are some Natchez with Chandler blueberries from my garden.

Typical harvests for me are rather large. i have gallon bags and bags of berries still in the freezer.
These are mostly black, red, yellow and orange raspberries with a few blackberries and a few strawberries.
