I bought a small torch light bulb one hour ago as my old one was faulty after I connected it to a 15V battery.

Now, it is quite different from my old one, not exactly the same in some manners.

For the old one, it can endure a voltage of 2.4V and so does my new one.

However, a label " 0.8A" was on the old one but "0.5A" is on the new one.

What does it mean? I guess it probably is the ampere of current passing through the circuit with a voltage of 2.4V with the presence of this bulb. I guess so.

By the way, I have no idea on which bulb can give a brighter light.

I think the new one could be brighter as the resistance is higher, am I correct?

No, With a higher resistance less current will flow and less light will be emitted. The 0.5A is the max current that the bulb has been tested with. Your new bulb is not as powerful as the old. Your old bulb is almost 2W the new is 1.2W.

The good news is that the battery will last quite a bit longer. A 2.4 volt .5 amp bulb is still going to be pretty bright, too.