Curved vs straight traveler

[Only Time]

Full disclosure, we sell and manufacture travelers.
Travelers curved in the vertical plane with the outboard ends lower than the center were made that way to be aesthetically pleasing to the eye. It would typically match the curvature of the cabin top.
Travelers are curved in the horizontal plane to match an equal radius from the mast - thus giving you equal tension on the boom at all times (as mentioned above, often seen on wider boats like a trimaran.
Ideally a track curved vertically, slightly upward on the outboard ends and curved horizontally, equal to a radius from the mast, will give you the best performance. When you let a traveler down on a windy day, it is typically to "dump" the sail, thus you want to open the leach when the traveler is lowered. If the traveler curves downward on the ends it will be closing the leach more (just the opposite of what you want).
The downside to a curve traveler is the limitation on the size of the traveler car so it will slide on the curves and not bind. Our traveler cars consist of 2 shorter cars to enable you to have a curved track.
For the average cruising sailor, my suggestion is a straight traveler as it will save you money and most people do not "work" the traveler sufficiently to take advantage of curve travelers.
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