: The reason I moved away from the Veritas jigs was because the ones
: I had had a tough time properly holding tapered tools and mine
: was tricky to use on my Japanese chisels and their 30 degree
: bevels. The Brian Burns jig worked much better for my stuff.

+1 Same here.
Also, with the Burns jig it's pretty easy to put a few degrees of bevel on the flat side of the blade, which saves a lot of polishing of the flat side.
I used to have to do that hand-held when I had the on-stone jigs like the Eclipse, or Eclipse variants like the Veritas.
But, they all work fine in their different ways.

I took a couple of courses with a UK & European-trained maker who hand-held for all his sharpening, and the results were near perfect.
For regular mortals, a jig is a big help!

The first time I used a really sharp chisel and plane was a definite 'Aha!' moment for me. After that, I always knew when it was time to stop and re-sharpen, rather than hacking onward.
;-)