My take on this is the first Thompson tool I used was so good that I never felt tempted to try D-Way or Carter & Son. Other very high quality marques include Stuart Batty tools (which I got to see close-up when I hosted him the time he came to give a workshop at my turning club), and HannesTools (he gets his tool steel from Doug Thompson).
I suspect that if I'd tried one of the others first, that would have been my choice going forward.
I own Thompson bowl gouges, scrapers and detail gouges. I own Carter & Son Bowl gouge and have used their detail gouge. As far as how long they hold an edge they are both excellent and I wouldn’t recommend one over the other As they both are excellent and hold an edge longer than other tools I own. What it boils down to for me is the flute shape on bowl gouges and detail gouges so I use them differently but am glad I own both.
I know people who own D-way and from what they tell me from their experience they are just as good as Thompson and Carter & Son. These folks have experience with all 3.
JimB has pretty well nailed it. If you go online and look at the demos given by various pro turners you will find all of the brands above and more. Jim's comment on flute shape is spot on--especially if you are using deep fluted gouges for bowls. Different grinds do better with different flute shapes.
If you're still looking for opinions poke around here a bit:
I know this is an older thread but I wanted to put in my .02 worth. What I think is more important than brand is the skill in sharpening. Thompson name won’t help one but if it isn’t razor sharp. I would sooner put money into a good sharpening system than the tools. Now if you can afford both all the better But a dull skew in a brand name isn’t a match for an ok skew in the hands of someone that can sharpen it..