more depends...
I'll give you some examples to explain this:
a 1.2V bulb, ~1W, ~0.8Amp: 3 configurations below:
1. 1 AA alkaline cell. bright and white at first, Runs for many hours of continually dimming light. Somewhere around the 1 hours mark it reach 50% output and from there it is downhill for a few hours longer.
2. 2 AA alkaline cells wired in parallel. voltage is still 1.5V, but with double the capacity(amp hours) Runs slightly brighter than the above example because the 2 cells in parallel have a lower total resistance under the load of the bulb. The result is each cell works about half as hard, and the voltage stays higher longer. The initial "bright white" output will last more than twice as long, and the trail of diminishing light will also last slightly longer than double the number 1 example. This is because you have twice as much power stored- but it is being released at about half the rate by each cell, the cells deliver a better overall performance when they aren't worked as hard.
3. 2 AA alkalines in series: the cells are now in series, the voltage is now 3V. The bulb simply blows immediately because the filament can not withstand the higher input voltage. As you increase voltage across a filament, more current *tries* to flow. A filament designed to to tolerate a watt of power doesn't do so well when you try to shove 2W through it- gets too hot.
Ok.. now lets step up to a 2.4V bulb, but cut the current in half, 0.416Amp. This is still a 1W bulb like the examples above, but it needs a higher input voltage to run at 1W because the filament has been designed differently.
1. 1 AA alkaline cell: the input voltage is only half the ideal voltage for this bulb with 1 cell. The result is a very dim light that puts out of most it's energy in the form of IR heat energy rather than light. This is because the filament doesn't get hot enough at this voltage to make much light.
2. 2 AA alkalines in parallel: The output would be about the same as above(slightly better), but since twice as much energy is stored, it would continue to be a very inefficient bulb for about twice as long. It's now, a longer lasting space heater. lol...
3. 2xAA alkalines in series: now we're up to the appropriate input voltage for the bulb. The bulb burns nice and bright. The output and runtime charts for this setup would look identical to the setup in example 2 under the 1.2V bulb.
ok... now lets look at some more examples:
the 2.4V bulb described above: but now we are going to run it on a single CR123 instead of 2 AA alkalines in series. The CR123 is a 3V lithium cell with 1300mah capacity. a AA alkaline is about 1.5V with about 2800mah capacity. However. The performance of these cells is heavily effected by the load they are under...
When we combine the 2 AA cells in series, the capacity remains the same, it's still 2800mah capacity. but the voltage is 3V instead of the 1.5V of a single cell.
(When we combine the 2 AA cells in parallel the capacity adds up, it's 5600mah at 1.5V)
now there is more to be considered.... back to our example of the 2 AA cells in series compared to the CR123...
if you have a look here
http://www.candlepowerforums.com/vb/showthread.php?t=64660
you see that alkaline cells do not perform anywhere near their rated power when delivering a 0.5A load.. which is pretty close to the load of our bulb here. Most of the cells only delivered about 1500mah capacity. Also notice the discharge curves drop very rapidly, the voltage keeps going down and down and down... this would result in a light that would just keep getting dimmer and dimmer and dimmer.. This is how most flashlights behave.
now take a look at this
http://www.candlepowerforums.com/vb/showthread.php?t=67078
The discharge graphs there show that at 0.5Amp... most CR123s deliver about 1500mah. also compare the voltage over time on these charts.. notice how the lithium cell (CR123) stays nice and flat throughout most of the discharge compared to the alkalines... Since it takes 2 AA cells in series to get the same 3V that the CR123 cell already has, and since the 2800mah alkaline cell only actually delivers about 1500mah into a 0.5A load, You can actually get the SAME AMOUNT of POWER out of a single little dinky CR123 cell, as you can out of 2AA cells.
Now... at very low power demands(like a clock), 2 alkaline AAs will have more energy than a single CR123, but when you get into flashlight power territory, lithium cells are much better.
And I keep hearing that Crees can be driven at 1A, how many ampere is a regular AA? CR123?
cells are not rated in amps.... maybe by reading the above you will get a better feel for this. The current that flows through an LED is determined by the input voltage. a CR123 or AA would barely move any current at all through an LED because it's not enough voltage to get things moving. Diodes have bizarre characteristics, they operate in a tight voltage range. Too little and practically nothing happens, but slightly too much and TOO MUCH happens, "pop."
Batteries are rated in Volts, and Amp/Hours.
if I have a cell that is rated 1.5V, and 2 Amp/Hours. Then I could say that I have a cell that can deliver 2 amps for 1 hour at 1.5V before "dieing"... however, this is rarely the case. A more appropriate way to describe a cell is this:
I have a cell that is rated for 1.5V, and 2.8 Amp/Hours. But the only way I can get 2.8 amp hours worth of capacity out of it is to stretch the test out to MANY hours to reduce the current demands on my cell, because at 2.8amps, my cell falls on it's face and performs very poorly. So I test my cell at a 280ma for 10 hours instead, Which is happily delivers. This is how I arrive at calling it a 2.8Amp/Hour cell.
Some cells can deliver more current than others as well. CR123s can deliver about 2.5amps. They run about 20 minutes at this output, sometimes going into thermal runaway. Alkaline cells could probably never achieve 2.5 amps. SilverFox Tested some D size alkalines at 3 amps... the result was about the same capacity delivered as a AA at 0.5A, pretty bad.
What makes lights bright is more power, more efficiency, or both. Battery configurations don't always decide this. The battery chemistry chosen for the light has a much larger impact on brightness because some chemistries like lithium can deliver much high power without falling on their face.