There isn't necessarily a consistent difference in longevity or quality between LEDs and "regular" bulbs. The most consistent difference is that of color temperature and spectrum.
LED lights are newer. They are solid state electronics that, when well designed and decent quality, can run for a very long time. Unlike traditional bulbs, they tend to lose brightness over time rather than simply burning out. They also tend to produce very narrow bands of frequencies of light and white LEDs are often a combination of other color LEDs used to produce a white like light.
The main advantage of LEDs is their low power consumption and low level of heat. They can often be relatively small and bright without being a fire hazard. Portable packs that can run off battery become a much easier possibility.
The main disadvantage is the aforementioned narrow spectrum. Since a digital camera is also only sensitive to 3 main bands of light (red, green and blue), if the spectrum produced by the LEDs does not overlap nicely with the spectrum of the camera, then things can look fine to the naked eye (which takes in many different colors of light) but can end up looking very weird or even not come out at all to a digital camera. It is important to make sure that the LEDs you choose are compatible with digital cameras.
This same spectrum limitations also often gives LED's the impression of being more harsh or producing a less "warm" light, though improvements in spectrum coverage have helped this greatly. It's also worth noting that the quality of the LEDs makes a huge difference on the actual quality of the light they produce.
Traditional bulbs on the other hand are less efficient and produce more heat, but produce a more complete spectrum of light. They will often provide better overall results on the cheaper end since they are less technically complicated and simple bulbs produce a fuller light spectrum than cheap LEDs (which are typically more expensive anyway).
That said, not all traditional bulbs are created equal either. There are an array of different types of traditional bulbs. Each different type has it's benefits in terms of color spectrum, temperature, cost and power. The traditional bulbs won't generally last as long as LEDs, but they will often be cheaper as long as size and portability isn't a concern. Portable battery operated packs tend to get much more expensive though since the traditional bulbs require orders of magnitude more power.
In the long run, deciding on a lighting technology really depends on what you need to accomplish and what kits are available in your price range. LEDs are generally ideal for portable and efficient lighting (and also may be able to alter their color temperature). Traditional lights tend to be preferable for getting the most light possible at the lowest price when other factors aren't a concern. There isn't a right or wrong answer between them. Look at what's available in your price range and choose based on the reviews of the products that fit your needs.