I'll break it up by caliber.
For 357 magnum, my two favorite double actions are the Ruger GP100 and the S&W model 27. There's nothing wrong with the 686, but the model 27 is classic. I never could warm up to a full lug barrel, and the model 27 is the original magnum before magnum was cool.
A lot of people will talk about the S&W triggers, and they are good, but in my experience they are not better out of the box than a Ruger GP100. There are some differences. The S&W uses a wide flat trigger where the Ruger uses a narrow rounded trigger. Both work fine for me. The single action pulls are good in either gun, and good gunsmiths can make either model extremely good. The S&W seems to have a slightly shorter double action pull, both models can be very smooth.
Both are very tough revolvers that will hold up to a long life of full power 357 magnum. Both have plenty long cylinders that will fit any reasonable bullet. Both have the same 1:18.75" twist rate, which works fine for most bullets. The only downside is if you wanted to shoot 220+ grain bullets, a 1:16 works better. Most people are shooting 158-200 grain bullets, which work great in these.
My preference is for the 5" Lipsey special half lug GP100, or the model 27 with 4", 5", or 6" half lug. I love a blued half lug.
When looking at 44 magnum I really like the Ruger Redhawk. It, and the super redhawk are the biggest and toughest 44 magnum double actions ever made. They have very generous cylinder lengths, and they handle 300+ grain bullets easily. 355 grains is not a problem either. The downside to the regular Redhawk is the trigger is not something a lot of gunsmiths know how to deal with. The single action trigger is just like any other, they can be very good. Out of the box most Redhawk triggers are not great, more like 5 pound SA pulls. The double action is what it is, they aren't too heavy, but they stack. It's not bad, but it's not the best out there. Lighter action springs can help, but it takes trial and error. The Super Redhawks are very similar to the GP100. They can have really nice triggers, and they come out of the box pretty good. The only real downside is how ugly they are.
S&W model 29 is an ok 44 magnum. They can't handle a high volume shooting of full power 44 magnum like a Redhawk can. Another very common issue is cylinder skipping where the cylinder stop lets the cylinder rotate under recoil. There are extra power springs which help, but do not completely eliminate the problem. If you never intend to shoot anything but 220 or 240 grain bullets, then no big deal, they work great with that. If you intend to shoot 260-300 grain bullets, then you can make them work. If you want to shoot 300+ grain bullets, you are probably going to be disappointed.
If you are ok looking at the used market and not scared of the prices, try to find a Dan Wesson 44. Those are sweet guns, probably the best ever. Great triggers, solid guns that hold up to a ton of shooting. They are switch barrel revolvers, so you often find them with multiple barrels.
My preference for a 44 magnum is the 5.5" Ruger Redhawk, but I'd love to have a Dan Wesson 44 with 6" half lug.