If it does, Would the moon receive more radiation than earth?
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Yes, to both questions. The Moon does not have an atmosphere to filter sunlight before it strikes the Surface like Earth does. All of the Moon's light is reflected sunlight.
"...Science tells us that every square meter of the earth's surface, when exposed to direct sunlight, receives about 1000 watts (1 kilowatt) of energy from the sun's light. Depending on the angle of sunlight, which changes with the time of day, and the geographical location [see map below], the power of the sun's light will be somewhat more or less than 1 kilowatt-hour per hour for every square meter of the earth's surface exposed to the sun. ..."
http://www.americanenergyindependence.co…
http://www.wisegeek.com/what-is-the-sola…
"...The solar constant includes all types of solar radiation, not just the visible light. It is measured by satellite to be roughly 1.361 kilowatts per square meter (kW/m²) at solar minimum and approximately 0.1% greater (roughly 1.362 kW/m²) at solar maximum.[4] The actual direct solar irradiance at the top of the atmosphere fluctuates by about 6.9% during a year (from 1.412 kW/m² in early January to 1.321 kW/m² in early July) due to the Earth's varying distance from the Sun, and typically by much less than 0.1% from day to day. Thus, for the whole Earth (which has a cross section of 127,400,000 km²), the power is 1.740×1017 W, plus or minus 3.5%. The solar constant does not remain constant over long periods of time (see Solar variation), but over a year varies much less than the variation of direct solar irradiance at the top of the atmosphere arising from the ellipticity of the Earth's orbit. The approximate average value cited,[4] 1.361 kW/m², is equivalent to 1.952 calories per minute per square centimeter, or 1.952 langleys (Ly) per minute...."
http://en.wikipedia.org/wiki/Solar_const…
"...Science tells us that every square meter of the earth's surface, when exposed to direct sunlight, receives about 1000 watts (1 kilowatt) of energy from the sun's light. Depending on the angle of sunlight, which changes with the time of day, and the geographical location [see map below], the power of the sun's light will be somewhat more or less than 1 kilowatt-hour per hour for every square meter of the earth's surface exposed to the sun. ..."
http://www.americanenergyindependence.co…
http://www.wisegeek.com/what-is-the-sola…
"...The solar constant includes all types of solar radiation, not just the visible light. It is measured by satellite to be roughly 1.361 kilowatts per square meter (kW/m²) at solar minimum and approximately 0.1% greater (roughly 1.362 kW/m²) at solar maximum.[4] The actual direct solar irradiance at the top of the atmosphere fluctuates by about 6.9% during a year (from 1.412 kW/m² in early January to 1.321 kW/m² in early July) due to the Earth's varying distance from the Sun, and typically by much less than 0.1% from day to day. Thus, for the whole Earth (which has a cross section of 127,400,000 km²), the power is 1.740×1017 W, plus or minus 3.5%. The solar constant does not remain constant over long periods of time (see Solar variation), but over a year varies much less than the variation of direct solar irradiance at the top of the atmosphere arising from the ellipticity of the Earth's orbit. The approximate average value cited,[4] 1.361 kW/m², is equivalent to 1.952 calories per minute per square centimeter, or 1.952 langleys (Ly) per minute...."
http://en.wikipedia.org/wiki/Solar_const…
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Likely that long answer is correct except the 1000 watts is maximum occurring in June or early July in the Southern part of the Northern Hemisphere of Earth. The lighted portion of the Moon receives about 1360 watts per square meter for about two weeks followed by two weeks of darkness, which makes the average about 600 watts = about double what Earth's surface receives on the average. The total energy received by the moon is smaller by several times as the moon has much less surface area. The moon's surface receives about as much ionizing radiation = dangerous radiation as Earth, due to lack of atmosphere and magnetic field, so humans on the moon need to limit their exposure or be at high risk for cancer. Neil