wich brand of rechargable batteries delivers charge the longest before needing to be recharged, does the answer depends on the type of...

The life of a rechargeable battery depends on several
things.  It will depend on the type of rechargeable battery, the quality of materials
used, and the device you are using the battery in.

There are two main
types of rechargeable batteries.  The first is nickel metal hydride batteries (NiMH). 
These batteries can form a memory; this means that if the battery is recharged before it
is fully dead, it can eventually be unable to hold a full charge.  However, these
batteries are less expensive than other types.  This is the common rechargeable battery
when talking about standard sizes like AA.

The other type of
rechargeable battery is a lithium-ion battery.  These batteries cannot form a memory and
hold a much more powerful charge.  This is the type of battery typically found in
cameras, cell phones, and other electronic devices that come with a rechargeable battery
installed. 

The length of the battery life is going to depend on what
you are using it in and how you are using that device.  Purchasing a charger that stops 
sending power to the battery once it's full will increase the life of rechargeable
batteries.  See the links below for more information.