On my Infinity Ultra, I measured 15,000mcd with an alkaline AA, and 16,000mcd with a lithium AA.
So the lithium *is* brighter, but not tremendously so.
Let me check my Ultra-G and see what happens...BRB...
17,100mcd on an alkaline, 21,200mcd on a lithium.
So the difference is a bit more significant, but not tremendously so.
The same two cells were used in both of these tests.