I would say aesthetics, heat output, cost and energy efficiency are some of my considerations when I specify under-cabinet lighting. Different fixtures "throws" different lighting spreads. For example, puck lights provide a more directional lighting output and gives a more dramatic ambience. Light bars gives off an even spread throughout the surface area it lights but can sometimes give off a more institutional feel. Fixtures with xenon bulbs creates a warmer color/feel and ambiance but they can get hot. If you place say a bowl of candy or a plastic container close enough to the fixture, it might melt. Under cabinet florescent lights give off a "brighter" and more "functional" light...some gives off heat but not as much as xenon bulbs...and again it creates a more institutional feel. LED strip lights have a cooler color spectrum (more cool blue) but does not give off any heat and will last you "forever." Downside is they can be quite expensive. Hope this helps!

And the often overlooked, but least expensive, not hot, even light source would be rope light.