fun stuff eh... I can *probably* explain what is happening: In the process I'll be throwing in other tidbits here that will help explain more un-asked questions along the way
3AAA powered LED lights are getting a "free ride" of sorts. Since the set of 3AAA cells delivers power very close to the Vf of many LEDs while under a load, they can be used "direct drive" or with nothing more than a small resistor in line. The result is no driver being required. It's almost guaranteed that if you buy a 3 cell LED light, it is taking advantage of this coincidence and fixing whatever minor variation there is with a simple resistor: So adjusting the power source even slightly, can have a substantial impact on the behavior of the light, since the performance of the light is built around a delicate balance between the battery pack, a possible resistor, and the Vf of the LED/LEDs.
Keep in mind that an LED is, a diode. It doesn't behave like a "normal" resistive load. The Diode is very sensitive to input voltage. even just slightly higher input voltages can result in substantially higher current, different LEDs react to voltage variation more violently than others.
The Luxeon series LEDs have a "gentler" angle of attack on their response to voltage input than most 5mm LEDs. For example, Taking a LuxI: Lets say the LED operates at 350mA with 3.6V applied (~1W), and in order to "bump" it up to 700mA you have to boost voltage to 4.1V (~3W).
LuxI lights are based on the same die as a LuxIII, only difference is that a LuxIII has a better thermal path both can handle more than ~1W and 3W respectively within reason. Provided the heat doesn't get too far out of control, a LuxI will handle 2-3W operation without much trouble, and a LuxIII will handle 4-5W operation without much trouble.
A 17500, while quite similar to a bank of 3AAA cells, does behave differently. From a fresh charge, a 17500 can hold above 4V into the loads we can expect in these lights for at least 10-30% of it's discharge, a set of 3AAA cells will, at these loads, only be delivering about 3.6V give or take. I must stress though that with alkaline, there is an initially very high level of performance, probably over 4V total just like the 17500, but it only lasts for maybe 30 seconds at these loads, it drops to a more reasonable ~1.2V per cell pretty rapidly and then continues falling from there.
Anyways: The 1W/3W Luxeon lights, when driven by the 17500, do get driven a little harder, but not enough to cause any substantial concern. Lets say in the 1W lights the LED *normally* sees 3.6V, and now, with the 17500, through the resistor, it is seeing 3.75V, sure it might be running at like 2W for awhile, but it's just not that big of a deal.
Anyways, lets switch gears to the 5mm LEDs, these suckers, might operate at their rated 20mA at 3.6V, but rocket to 100mA at 3.8V. These configurations are usually resistored, but not always, a LARGE bank of 5mm LEDs, like say, enough to draw 1A or more safely, will almost always "draw down" a set of AAA cells low enough to balance out and not overdrive the LEDs too bad. Changing the power source here, can have a massive impact. Assuming a 28 5mm LED array, it should draw about 0.5A all together with 20mA per LED, even a slight increase in voltage would make this thing try to draw as much as 3-5amps or more, but since AAA cells just can't handle that kind of current, the voltage will always sag to a reasonable level for the LEDs, perhaps as high as 1A (or around 40mA per LED) on really fresh alkaline cells, but never much more than that. The problem with the 17500, is it can easily deliver several amps while holding above 3.7V. Which results in massive overdrive in this configuration.
Does that make any sense?