AA "Lithium" batteries (Li-FeS2) like the ones you used and AA "Alkaline" batteries have the same nominal voltage (1.5V) so you shouldn't see a difference in brightness between fully charged batteries of either type. Where this type of lithium battery rules, though, is in the total capacity. At a constant 500 mA drain, alkaline batteries will hold 1800-2600 mAh versus lithium batteries with somewhere between 2700-3400 mAh. In high-discharge applications, you can see up to 2.5x longer life with the lithium cells versus alkaline. They also store better due to much lower self-discharge rates (think storage in the 10-20 year range with little to no effect on capacity).
Also, don't confuse these "Lithium" cells with the CR123A lithium batteries often used in high-brightness flashlights (think "Surefire") and such. The CR123A uses a Li-MnO2 chemistry, producing a terminal voltage of 3V (instead of 1.5V as with the Li-FeS2), and work better in low-drain applications. They don't like high current drain applications, but can deliver brief "spikes" of high current effectively. The CR123A will also self-discharge at high temperatures so are more critical of storage.