I think that it is important to remember that Princeton Tec designs their lamps for camping and outdoor activities - meaning that they are made for around the camp or on the trail - back country. In these environments, burntime and usable light are more important than shear power. It does not require extreme amounts of light, but basic light. The burn time is an even 40 hour plus hours (mine burns roughly 60 on alkalines) - it maintains a constant output for the life of the batteries.
I spoke to Ed Viesturs last year - he uses the Matrix for around the camp and has taken it up Everest. His comment is that it is a great light, but for any technical uses, LEDs are not going to do it.
They say the thought was to give adequate light for backpacking with the most burntime possible - if they bumped the voltage, the burntime would decrease (see what happens if put it in the Tec 40 - a bit brighter, with little more than half of the burntime)
The Tikka is designed with a different thought. Petzl uses no step up and it burns bright for maybe 9 hours and slowly dimishes for another 9, but drastically drops off there after. Petzl went for price, Princeton considered technology.
They are both good lamps, it just depends on what you are planning to use them for.