There are several different systems of rechargeable battery powered light systems that can be used for bicycles. Each of them has advantages and disadvantages, and some systems are undeniably safer than others.

Standard Battery Lights
While using low cost battery powered lights isn't legal in all areas, it is a good system of lighting if you aren't going to be biking often in the darkness. These lighting systems are generally very inexpensive and can be purchased nearly anywhere. These systems are also useful in that they can be easily transferred from bike to bike.

Rechargeable Flashlights
I would personally never recommend riding your bike at night with only a flashlight attached to the handlebars. While this does provide a bit of light and visibility it is an unreliable method that could result in dire consequences. Though there are some advantages to using this lighting method like versatility and portability, the disadvantages far outweigh them. Disadvantages are numerous, especially if you are going to be biking in a busy area. Disadvantages such as limited visibility and unreliability top the list, but there are also smaller complaints, such as the flashlights being heavy or expensive.

Rechargeable Halogen Systems
While halogen lights aren't legal in all areas, this form of lighting is a bit more sophisticated than the previous systems. This lighting system consists of attaching halogen headlights to the handlebars of a bicycle and powering them with a battery pack. This lighting system emits a very bright light, which can sometimes prove to be harmful for oncoming traffic, hence the illegal element in some areas. This bright light is beneficial to the biker however, giving them a greater visibility. The halogen lamps necessary to provide the light are generally inexpensive and battery packs can attach to several lamps at one time. However, there are a few disadvantages to using a halogen system. The lamps aren't specially made for road use, which could cause visibility problems. There is also the issue of dealing with batteries in general. Making sure that your battery is completely charged is a common concern, as well as the weight of the battery pack. These systems are great if you aren't going to be biking long distances, but if you are a more avid cyclist you may want to look into a generator lighting system.

Rechargeable H.I.D. Systems
The final system that will be mentioned in this article is the rechargeable H.I.D. system. Currently H.I.D. lights are the brightest and safest lights available for bicycles. They are also relatively expensive and don't have very long lives. Again, if you are using these systems on the road it is best to adjust your lights to avoid "dazzling" oncoming traffic.