OK, quick answer... there is no quick answer. I have Atlas, Peco and Shinohara turnouts on my layout. The advantage to Atlas is that you can get them into operation fairly quickly, if you don't mind the quickly attached switch machines on top of the board. (There are under-the-board attachments for Atlas switch machines.) Atlas also have the advantage of not having to mess with wiring if you don't care about having directional powering of the two routes. Atlas #4's are really #4-1/2's. I have had some problems with the Mark IV #4 points not being in gauge on the diverging route. Disconnecting the metal point from the plastic throwbar and using a flat Swiss needle file on the back side to remove metal further toward the pivot, and then reconnecting the point and bending the point until it passes an NMRA track gauge, solves the problem. Don't seem to have it on the #6's and #8's.
You don't have this problem and have a more realistic-looking turnout with Peco and with Shinohara turnouts, but they require separate switch machines. The Peco turnouts have the advantage of permitting manual operation, as they have a snap spring that holds the points in one position or the other. I have found some problems with the Peco switch machines not throwing the points readily, and you can't just remove the turnout throwover spring, since the Peco switch machines don't have any positive holdover on their own. I haven't used them myself, but I would suspect Tortose switch machines would work fine with the Pecos after the little throwover springs are removed. Peco's come with a choice of either InsulFrog (insulated frog) or ElectroFrog (frog connected to the other rails. This has the advantage of having power to the individual route selected by the points, though you may want to use accessory contacts on a switch machine to insure good power feed. Shinohara turnouts do not hold their position without an external means to do so, either a mechanical ground throw, or a switch machine.
As I've said, I use all three in various places on my 14' x 14' layout, depending on what I had on hand from my previous layout and what the geometry dictated. I've also used Kemtron and Tenshodo/Sinohara switch machines. (The latter are very positive in action, if you don't mind the solid CHUNK! when they actuate.) I'm not even sure these are made anymore, but I've had them on hand, and bought nine of them "surplus" on e-bay.
Hope this helps.
So how would you rate turnouts in order from best to worst?
