Looking at the data sheets, at 700mA, a luxeon III has a vf of 3.7v and a rebel 3.4v. How much of an impact will that have on current draw? I have to say, this is new to me, that if I replaced an older emitter with a newer, more efficient one, the current draw would go up. Got a link to where I can learn more about it?
not taking into account battery resistance you could consider the LED like a resistor although they don't exactly act like one in every respect they are close. You can calculate the difference using Ohms Law E=IR where E = voltage, I = amperage, and R = resistance (in ohms).
3.7v @ 700ma R=E/I or 3.7/0.7 = 5.29 ohms
3.4v @ 700ma 3.4/0.7 = 4.86 ohms
depending on the initial voltage if you were to run both at 3.7v you
would get this
first one would be 700ma using I = E/R for the second one (3.4v Vf)
we would get 3.7v/4.86ohms = 760ma or about 8.6% higher current draw.
I would say that this could make it run perhaps 8-10 percent shorter time but the LED would put out slightly more lumens due to the 8.6% higher current applied to it. The power would be as follows
3.7v 700ma = 2.59watts
3.4v 700ma = 2.38watts
3.7v 760ma = 2.81watts so the led would be driven about 18% harder than spec (extra 0.3v, extra 60ma)
now driving it 18% harder it will produce more heat and slightly reduce efficiency due to extra heat loss, that I cannnot calculate without some sort of equation or extrapolating from lower to higher outputs light vs current.