" Highly efficient IC driver keeps the power stable ..."

There's your problem, coupled with poor design. There's a chip banging on and off, that's causing electrical noise.

For grins, wrap the light in aluminum foil (except don't short the endcaps to each other) and try it again.

Also, does it cause interferrence only when the dome light is lit?

The chip is actually turning the leds on and off very rapidly - so fast, you can't see any flicker. That means there is current starting and stopping many times per second... like 10,000 times (10Khz). Sometimes, you can stick your ear near it and hear a high pitched whine. That's all well and good for efficiency, but each time it switches, there's a pulse in the line, and it'll ring like a bell with many harmonics extending up into the RF range - that's the noise that interfers with your radio transmitter. Killing that noise is where the good design would come into play; it may take just one capacitor or inductor of the right value in the right place. Testing parts so they don't interfere is part of good engineering, but the fast buck aftermarket places don't always bother with it. I've recently spent over $10K at the test lab getting my product through EMI testing.

Without getting deep into the specifics, I can't comment on the other product. For $15, try it and see.