Fluorescent light bar lights typically include the ballast and other drive electronics embedded into the fixture, making the installation and wiring somewhat more straightforward when compared to puck lights. Most fluorescent fixtures for under cabinet use are of the T5 variant, which provide a smaller profile.
One significant downside of fluorescent strip lights for under cabinet use is their mercury content. In the unlikely but still probably event of a lamp breakage, mercury vapor from a fluorescent lamp will require extensive cleanup. In a kitchen environment, toxic chemicals like mercury are definitely a liability.
LED strip and bar lights are now viable alternatives. They are available either as integrated LED light bars or LED strip reels. What's the difference?
Integrated LED light bars are typically rigid "bars" that are 1, 2 or 3 foot in length, and have LEDs mounted inside of it. Oftentimes, they are marketed as "direct wire" - meaning that no additional electronics or transformers are necessary. Simply plug the fixture's wires into an electrical outlet and you're good to go.
Some LED light bars also allow for daisy chaining, meaning multiple light bars can be linked together consecutive. This also makes installation easy, since you don't have to run separate wires for each fixture.
What about LED strip reels? Typically, these products are more suited for those comfortable with low voltage electronics, but nowadays a complete line of accessories and solutions has made them much easier to work with.
They come in 16 foot reels, and are flexible, which means they can be installed on non-flat surfaces and make turns around corners. They can be cut to length and, and simply mounted onto the underside of virtually any surface.
Especially when lighting a large area, LED strip lights can be a much more cost effective solution. Even if you're not comfortable with electronics, it may be worth having a contractor come in and give you an estimate, as the final cost may not be so different from LED light bars, and the final lighting effect is very pleasing!