There is a conversion from watts of radiant power to lumens. However, it varies with wavelength. Lumens per watt is lowest at the red and blue extremes, going right to zero at the point it becomes ultraviolet or infrared, and is highest in the middle, at a particular green color (555 nm). At this peak, it's 683 lm/W.
White is a mixture of colors, and as you'd expect, less than 683 lm/W. Theoretical maximum peaks around 370 lm/W of white light, depending on exactly what your 'white' consists of.
If an LED (or any other electric-powered light source) converted every bit of electrical power into light, this is what you would get. But some of the electrical power is converted to heat, resulting in efficacies lower that the theoretical limits mentioned above.
Typically the power rating of a lighting or indicating LED is the input power, not the output power. Output is typically spec'd in some measure of brightness or luminosity - lumens, candlepower, candellas, etc. Exceptions are deep blue, violet and ultraviolet at the lower wavelengths, and far red and infrared at the long end. This is due to the human eye's varying sensitivity to various wavelengths. Where we can see it well, we specify in terms we can see. Where we can't see it well, we need another way to specify it, and that typically turns out to be milliwatts.
So unless it says otherwise, your 450 mW LED is probably 450 mW input, and the output is something considerably less. If it's actually spec'd as 450 mW output, it's probably such a long wavelength that it won't appear bright.
How bright a light source appears is related to both the total amount of light output (lumens), and how focused the beam is. Spread omnidirectionally, one lumen gives 1 candlepower. Focused into a tight beam, it could be 100 candlepower or more.
Long story short: you need more information to compare these two LEDs. You'd need to know the wavelength of each, the beam pattern, whether 450 mW is input or output, and if input, you'd need to know either the efficiency or the efficacy of the LED. If you are missing even one of these, it will be impossible to objectively compare them on paper. The only way would be to observe them in operation. If the only thing you were missing was the efficiency or efficacy of the LED, you might be able to do some research and come up with a reasonable estimate. The others vary over such a wide range that a 'reasonable estimate' is not possible.
Sorry to rain on your parade :mecry:.