It's a common question we get asked!
The brightness of tape isn't determined the voltage but actually by the type of LED chip that is used, and the number of diodes per meter.
It is common for a 12V and 24V LED to have the same brightness, especially on short lengths of up to 5 meters. The main advantage to using a 24V supply is the fact you can run a longer lenght of LED strip before experiencing a voltage drop.
The advantages of 12V.
The 12V is a great option on 60 or 120 diode tapes, as they allow a more regular cut increment than their 24V alternatives.
For example the 120 diode 9.6W per meter led strip in 12V has a 25mm cut increment, whereas in its 24V form it can only be cut every 50mm. This is allows greater flexibility in getting the light to run edge to edge in the area that needs to be lit.
The disadvantages of 12V.
With 12V tape, you are limited to a length of 5-6 Metres depending on the wattage.
The advantages of 24V.
By using a 24V tape, you'll be able to run a longer length without experiencing a voltage drop.
Voltage drops gradually as it moves along the led strip, the furter it travels, the more it decreases - this can end up by causing one end of the strip to be brigther than the other.
By using a higher voltage tape, the length it can run a longer length, without voltage drop.
More powerful tapes such as 300 diode per meter single colour led strip lights and 120 diode per meter RGB colour changing strip lights, require much more power to run, 24V is the excellent option for this, 12V simply can't cope!
The disadvantages of 24V.
The cut increment increases compare to the 12V alternative. This is a small price to pay when you consider the advantages of running longer lenghts on one continuous run.