Lighting – change the light bulb to an LED multicolored light bulb

Are these the the type of motion sensors which use the neutral wire? A motion sensor needs power to work. Ideally it gets always-hot, and neutral, and then provides a switched-hot to the target bulb. Such a unit should work fine, I use them widely.

However some motion sensors are designed like old school dimmers - they are designed to work in old-style "switch loop" wiring which did not provide a neutral. They get power by placing themselves in series with the incandescent bulb - they allow a small amount of current to leak through, not enough for the bulb to light.

This totally falls apart with CFLs or LEDs because their switch mode power supplies do not play nice with that scheme. My suspicion is you have one of these.

You can get new sensor heads that do have neutral wires and attach in the same way (screw into a 1/2" knockout). I use them widely and they play nice with everything.

Or you can get entirely new sensor/lamp combos which are sealed, since the LED emitter is going to outlive us all. Some of those are 12V internally, i.e. the sensor runs on 12V as does the LED emitter head. 12V detector heads are much more economical than 120V ones.

Or you can slap an incandescent into one of the lamp positions. Or a resistor of appropriate size which has the same effect.

The first problem here is the "100W" claim, which you here treat as the reference standard from which to compare. Actually, it's the most dubious claim of the bunch, and has never been reliable. I suspect it's a common mistake for people to fixate on the "100W" number since it's a unit they're familiar with, and that's why manufacturers toss it on the box. It's time to get familiar with lumens. Seriously.

I went ahead and edited into your question their claimed lumens in italics. You can now see how different they are, in fact. Even the prices fall more in line once you are looking at lumens per dollar.

Now that you see lm/w numbers, you can see where Energy Star doesn't mean a whole lot when everything blows the doors off the mandated efficiency numbers, even no-name house-brands that took a ride on a slow boat.

The bigger issue is life-cycle quality. A lot of consumers have market blindness. If it's marketed aggressively at their favorite discount big-box, people perceive them as quality simply because they are plentiful. Nothing could be farther than the truth.

A big factor is losing brightness over time. The raw LED emitter business is dominated by 5 or 6 large companies who aggressively cross-license the technologies to make LEDs last a long time. More on that in this SE answer. It's about who makes the internal LED emitter chips, and less whose name is on the consumer product. (though obviously a Cree lamp will have Cree emitters, a Philips lamp Philips emitters etc.) You can look for blogs and Youtubes where electronics geeks do teardowns of the various brands.

The other factor is the quality of the electronic driver circuit - and cost is everything here. When the driver fails, the LED goes dark entirely. Well-marketed products are built to a price point - and that means cutting corners in the driver, where failures will not emerge for 1-5 years, after the warranty has run. And people get hoodwinked by what's probably a house brand "Euri" (did not check the Japanese meaning, clearly).