The straight style is more common in US home kitchens; the Y-shaped style seems to be more common in Europe. In the US there has been a trend of chefs and food writers evangelizing the Y-shaped peeler.

In my experience the straight style is more ergonomic for carrots and parsnips whereas the Y-peeler works better for potatoes, citrus, and other roughly spheroidal foods.

(I also use my [very sharp] Y-peeler for shaving hard cheeses into flakes so sure, I guess it is a cheese slicer too :) )