50W LED with 10W power equal to 10W LED at full power?
All else being equal, yes. Of course, all things are never equal.

First, the lower-power unit will probably be physically smaller than the 50 watt, and this will include the light-emitting area. If you look directly at the LED while it operates, there is a good chance that the lower-power unit will appear brighter, since it is emitting light from a smaller area. However, the appearance is irrelevant. What counts is the total light emitted, not the power density per unit area.

Second, (again assuming a physically smaller LED) heat sinking is likely to be more effective on the higher-power LED. At the same power it is likely that the low power LED will run hotter, and this will reduce its efficiency somewhat.

Finally, the power rating for an LED refers to the total input power, not the visible output. So the two LEDs may not use the same process, and may have different intrinsic efficiencies.