10 3W RGB LEDs in series control current
You are doing something wrong. I suspect your either your wiring (you may be using much too small wires) or your power supply is not behaving correctly. 

When you connect all 10 LEDs to the 5 volt supply, you claim a current draw of 2 amps. That is .2 amps per LED. In that case, a 4.7 ohm resistor will drop just about 1 volt, leaving your LEDs dropping 4 volts. And that is not possible. Without a picture of your setup, I suspect that you are not using thick enough wire to connect to your power supplies, and the wire resistance is causing you problems. You may even be on the edge of melting your insulation. When you do your high current tests, do you smell something funny?

In addition, if you ever do get the current right, you will kill your transistors. From the data sheet, the VCE(SAT) can be as high as 2 volts at 3 amps. Let's use this as a working number rather than 2 amps, since you also stated that a single LED will draw .4 amps, so with all of them working you should draw 4 amps, not 2. With a 2 volts drop on the TIP120, and a current of 3 amps, the transistor will dissipate 6 watts, and this is more than a bare TO220 package can handle. You must provide a good heat sink for your transistors, or change transistors to something with a lower voltage drop. As Asmyldof suggested, other transistors should be used. Personally, I'd recommend a MOSFET.