yes. you are right. the near linear discharge curve of Li batts provides a somewhat reasonable substitute for current regulation. i've tried it in unregulated headlamps and really like how much longer the light stays bright. however, Li batts are a more expensive option.
using alkaline batts, with some unregulated headlamps employing 3xAAA and running on max output, light output can be down to 50% in 30min to 2hrs due to the non-linear discharge curve of alk. batts. allowing the batts to cool for 10-15min every 30min, like cavers do, but they carry a backup-"primary" (not really an oxymoron) light source and so can afford to do this, will extend the time the batts can power the headlamp to produce bright light output.
also, Li batts in regulated headlamp will provide, in some cases, up to 4x the regulated output time. so, either technology "wins" with Li batts (it's the wallet that looses).
Info on Regulation for any who are interested:
i am a very big fan of current regulation.
however, there are some myths surrounding current regulation. any regulatory circuitry (whether voltage reg., curr. reg., or PWM [pulse width modulation] is parasitic in nature, drawing additional current from the power source in order to power itself - there is a lot of engineering effort put into making these parasitic losses as small as possible). while operating in the regulation band, the light will maintain near maximum output - a good regulation circuit can keep it w/i 90% or more of initial maximum regulated output. i've read of one curr. reg. chip that can keep it closer to 97%. some don't do quite as well as the 90%, some only 85%, after a short initial max. output period. often higher % regulators draw more parasitic current for their operation. generally, you don't get something for nothing.
IIRC, the Eos, using alk. batts, on max output (fortunately, IMHO, for most applications, medium output is all that is required) after far, far less than 30minutes continuous operation (within a few minutes continuous operation at max. current draw, IIRC) has dropped down to ~85% of max initial output (i believe/guess that much of this is due to the batteries heating up at hi-current draws - batts get hot => internal resistance of batts increases => drops voltage internal to the batt; smaller batts heat up faster). the human eye, under most circumstances the hiker is likely to encounter is probably unable to distinguish this 15% reduction in light output (25%-33% is a more reasonable value to notice a difference in light output under all but the most favorable conditions, IME). this 85% value might be a good trade-off, however. higher levels of regulation would undoubtedly employ greater parasitic losses to power the more sophisticated regulator, resulting in better regulation, but shorter regulated output times.
typically, current regulated headlamps behave in a small number of ways. as battery voltage drops and the regulatory period ends, one of the following typically occurs:
a) the light shuts off (allow the batts to cool down for 10-15 min and you will often get more light out)
b) the light flickers as an indication that the output needs to be lowered in order to maintain regulated output (Photon Fusion Freedom operates in this manner for instance)
c) the output is auto-magically "stepped" down to some lower regulated level, or very low regulated level output mode, so as to not leave the user in the dark (e.g. 1st gen. Photon Fusion).
d) the output is switched over to unregulated output ('a la several PT headlamps, Eos being one of them, PT Corona and PT Apex being two others that i am familiar with)
now, if an unregulated headlamp were compared side-by-side with the regulated one (assume also that starting light output was similar), the reg. headlamp would be drawing a bit more current to power the regulator ciruitry = parasitic current. at the point that the regulated headlamp lost its ability to regulate light output and switched to an unregulated mode of operation, the unregulated headlamp would be "burning" brighter. the unregulated headlamp has not had to suffer the parasitic losses that the regulated headlamp was subjected to. from this point on the unregulated headlamp is more usable than the regulated headlamp. sometimes, this difference is quite marked - even for 3xAAA headlamps i've seen graphs where it can be sometimes measured in hours.
PT's solution to the regulatory problem is a very fine solution. i really like it. reg output auto-magically switches over to unreg output. some older reg. headlamps just stopped working at that point, leaving the user in the dark, or switched over to a very dim, very lo output mode which was not real useful other than as a task light. the Eos switching over to unreg output still provides a fair amount of usable light for quite a while (measured in hours).
keep in mind, the PT documentation that comes with each reg. headlamp makes this quite clear, that while using Li batts will extend the reg. burn time b/f switching over to unreg output mode, it will not extend the TOTAL burn time. less power remains in the Li batts to run the headlamp in the unreg. mode of operation. with Li batts, the unreg time can be a small fraction of the unreg time that alk. batts produce since more of the batt's stored energy is used in the regulatory mode, leaving less available for the unreg. mode. this is not a criticism, just an observation. so, if you use Li batts don't count on as long a time of unreg. output as you prev. experienced if you used alk. batts - you could be in for a surprise!
so, let me clarify my earlier statement, if the TikkaXP is the KING of 3xAAA headlamps, then the Eos is the QUEEN of 3xAAA headlamps. ...and...
as any married man will tell you, we all really know who rules the roost!!
ok...seriously, from my perspective, while i really like regulated output and am disappointed that the TikkaXP is not regulated (see my Posts in other Threads and my ReaderReviews which mention this fact), the light output (and occasional BOOST mode use) plus the diffuser, puts it over the top for me. given a choice, if it's close, i'll go for regulation. the TikkaXP just nudges out the Eos for its other features. oh...perhaps if the Eos had a better/larger beam pattern it would still, for me, edge out the TikkaXP. the beam pattern in my Eos is a much smaller diameter as cp. to my TikkaXP & so is just a tad less useful, i.e. more "chicken walking" (i.e. head bobbing and turning) is req'd to spot lo-contrast, faded blazes on trees & rocks. that is, in some situations, you can't just move your eyes to "spot"/pick-out things/blazes; you must turn your head a bit (up-down, or left-right), to bring the small, very bright central spot of the Eos to bear upon tree trunks, rocks, etc. the TikkaXP bright central "spot" is quite a bit larger than the Eos & eliminates much of this "chicken walking". psychologically, one gets a more comforting feeling that nothing is being "missed" with the larger illuminated area - probably because less effort is required to make sure that you don't miss a trail blaze.
there certainly is very little to complain about with the Eos. it's a fine headlamp. my ReaderReview indicates this, and despite its relatively minor shortcomings, i gave it a 5.