Hi there BJE!
Interesting question. Historically, many Sheffield knives were produced by small cutlers, 'little mesters', who were effectively self-employed, and paid for their work by the large cutlers on a 'piece work' basis. The practice is still very much in evidence, and I think the larger existing cutlers buy almost all their work in. I've also long suspected that many of the blades are machine-ground using the same patterns, possibly even in the same place!
Taylor's do some nice up-market Lambsfoot knives, though personally I think they're overpriced. One of their cutlers also produces his own knives at even fancier prices. Their less expensive knives I think are bought in, and are essentially the same as the Rodgers and Arthur Wright knives. I can't speak for the present, but in the past their QC was a bit better than the others, and it's a historic firm, which hasn't just had its name sold on (eg Wostenholm, Rodgers), even if their once great factory is little more than a shell today. Recently Taylors have 'produced' a plastic handled budget line, the provenance of which I find questionable.
The Joseph Rodgers knives are sold by the Eggington Group from another factory that is essentialy no longer a factory (as Taylors). Since they don't make them themselves, you could very well get the same knife with a different stamp. Quality is very variable and QC practically non-existant - about the same as just about every other contemperary Sheffield non-cutom knife unfortunately.
There's Trevor Ablett, an ageing 'little mester', now using his own mark. His knives also vary in quality, the grinds in particular have been criticised here. He uses machine-ground blades much the same as the others, with the knives finished by hand, also much like the others. They're a little bit pricier, but cosmetically nicer than most.
I've had a couple of nice Arthur Wright Lambsfoot knives, but I had to sort through an awful lot of duffs to find them. If you get lucky, they're a nice knife, and with some work the blade will take a good edge. I've never been to the Wright works, but I understand old Mr Wright, who is in his 80's, still works there
Unless you want to spend some big money on one of the fancy Taylors, which will have essentially the same blade as the rest, but perhaps with some file work, I'd be inclined to suggest Trevor Ablett, or failing that, Arthur Wright or Taylors.
Prices will be in £ (Pounds) Sterling I imagine, but I don't know which site you're looking at. Feel free to PM me if I can help.
In Sheffield we have
Henderson's Relish on our chips, though I quite like
Tony's
Jack