This thread might help comparing the newer LEDs.
Basically, the Cree XR-E P4(3W is just the current it might be running at in a light) have double the efficiency of a Luxeon I, III, V, and K2 LED. The Q2-Q5 bins are even more efficient. A single Cree P4 should output about 180 lumen at 1 amp and around 3.4-3.8v, a single Q5 should output around 230 lumen at the same current. The Cree Q5 should be the brightest consumer single die LED available at this time(there are brighter ones but they aren't for sale). The Cree has a narrower emitting pattern then the Luxeon. Could be hard to solder and requires clipping the corners or removing the surface mount parts to prevent shorting if you are using the bare emitter.
The Seoul P4 uses that same die as the Cree and has similar efficiency. It has a similar emitting pattern to the Luxeon and is used by some to replace their Luxeon LEDs. It has around 200 lumen at 1 amp and 3.5-3.8v. The Seoul has phosphor problems with temperature and it also has a positive slug which might require isolation to prevent shorts with the bare emitter..
The Edison Opto is another LED that uses the same die as the Cree and has similar performance. IIRC, it has the exact emitting pattern of a Luxeon but will leave a yellow ring around the hotspot if used with a reflector.
The Luxeon Rebel is a surface mounted LED 1/4 the size of the Cree, though it has the same die size. There are many different bins of Rebels with the Rebel 100 being the brightest. If the Rebel 100 die and phosphor was used in a 4 die LED like the Luxeon V, you should easily get 800 lumen out of the LED at 1 amp.
I hope that I made sense.