Copper? I don't know nothin 'bout Copper.
Really, a Copper pill will transfer heat from the led much faster than Aluminum or Brass/Bronze. How much faster? I have no test data other than playing with this stuff for a long time now. By feel and my own experiences I would feel safe to say that Copper transfers heat about 1-1/2 times as fast as Aluminum. As an example, let's take a piece of Aluminum and say that by heating it with a torch, I can feel the Aluminum getting hot in 45 seconds. With the same sized piece of Copper I can feel it heating up in 20-30 seconds. I know, that's not the kind of test you want, but it proves to me, that Copper is much better than Aluminum, for heat transfer.
We've been down this road over and over, up one side and down the other. It is a proven fact that Copper transfers heat thru it much faster than Aluminum. Look at any chart on the subject and it will clearly show that. Look at led testing on Copper vs Aluminum stars and it clearly shows an improvement in getting heat out from the underside of the die.
Where the problem lies is, where is that heat eventually going to go? Unless you have made a light completely out of Copper, then it will contact Aluminum at some point. The smaller the Copper heat sink, the faster that will happen. I liken it to driving on a two lane highway and all of a sudden there's road construction and you are down to one lane, (for the next 14 miles). If that two laner was even halfway full, you are now bogged down in very slow moving traffic. Your mood worsens and you get hotter and hotter, because there's no relief in sight. This is what happens when a Copper pill runs into an Aluminum head. When the Aluminum acts as a road block, the Copper keeps getting hotter and hotter, with no relief. So, you will eventually get so hot that the led may fail.
Remember also, that since Copper has more mass, it will hold heat longer, once it's heated up, so if you run the light hard for so long that you can't hardly touch the Alunimum head and you quickly turn it down, the Copper pill is going to hold that heat much longer than the Aluminum head will.
Now, if you had just stuck to the Aluminum pill, the heat transfer, for all intents and purposes, would be slow, but smoother, as the pill to head transfer should stay at approximately the same rate. Will that be better? I don't think so, because the Aluminum is slower to take heat, the led will initially get hotter faster, than if it was on Copper.
General rule of thumb (for me), If you intend on hot rodding a light and pushing a led far above it's "normal output", you are asking for it to die sooner than later. We all do it and we all love it, but it's just stressing the led. Using Copper will give you higher initial output for as long as it takes for the heat to bottleneck, then it's just as bad, (or worse), as Aluminum after that point.
This is just my own thoughts and meanderings. I am not a scientific person. I learn from real life experiences and what little common sense I have left, tells me Copper does transfer heat much faster than Aluminum, but if it's going to bottleneck in a few minutes anyhow, is it really and truly any better?
I use it a lot! Why?
It's very easy to work with, when you are using hand tools. It can be heated to make it soft and worked to make it hard again. It is much heavier, therefore more mass in the same space. It looks Cool! I love the look of polished Copper! It takes solder like a duck takes to water. It makes the initial output of a high powered led more efficient, till the heat bottlenecks.
Each person has to weigh the pros and cons. The smaller the Copper pill, the less useful it will be. The larger/thicker the Aluminum head, the less effective the Copper pill will be. Ideally, I would want a large Copper pill with a large, but thin, Aluminum head, with lots and lots of deep fins on the outside, to take heat away from the Aluminum as best as possible from the surrounding air.
I'm done ranting and spell checking, time for bed.