Differences between any makes or models of LEDs can be discussed around certain parameters, so you need to understand what those parameters mean before comparing LEDs.
HP LEDs are typically compared based on brightness and spectrum. Basically, LEDs are either monochromatic (one color) or wide spectrum (white). The ways you compare brightness and spectrum differ based on the color of the LED. A white LED might be measured by lumens per watt (lm/w) for brightness and by a color bin that specifies a spot on the CIE1931 space, or less accurately by a kelvin temperature. When you are trying to decide which white LED is best, start by comparing LEDs that are similar spectrum (i.e. warm white vs. warm white, don't compare one vendor's warm white to another vendor's cool white). Also make sure the specs refer to the same operational parameters - you don't want to be looking at one LED's efficiency numbers at 350mA and another's at 1.5A. Then, compare the lm/w numbers - higher is better.
Comparing monochromatic LEDs is similar except the color is specified by a wavelength (nm) and intensity is sometimes specified in milliwats instead of lumens.
All that said, the cliff notes version is that, more or less, the best products from Cree are typically better performing than anyone else's best products. If you have specific bins and models of Cree to compare to specific bins and models of something from EPIStar, we can look at the numbers, but generally Cree's products are going to perform better.
That said, you can definitely build an effective rig with EPIStar LEDs, but it probably won't perform as efficiently as a carefully designed rig with Cree LEDs. Basically it's a balancing act between upfront cost (the EPIStar LEDs are probably cheaper) vs longterm operating costs (the Crees will probably be cheaper thanks to better efficiency).
It's also important to consider other factors, like beam width (some of the off-brand LEDs come with a narrower beam width, which gives the appearance of greater intensity since the light is focused on a small area). Also, optics availability - it sucks to build a rig, decide you want to play with different choices for optics, and then disover that the LED you picked doesn't have any optics available other than the ones you already have.