Van Allen belt radiation consists of high-energy electrons and protons in the inner belt, and high-energy electrons in the outer belt.
The most energetic electrons encountered along the trajectories flown by Apollo have an energy of about 7 MeV. The 7 g/cm shielding provided by the CM hull is about twice that needed to completely stop a 7 MeV electron. Electrons, therefore, were of no concern to Apollo as they were virtually all blocked by the hull.
At a given energy, protons are less penetrating than electrons. Therefore, virtually all protons on the low end of the energy spectrum were easily blocking by the spacecraft shielding. The only real concern from a radiation standpoint were the most highly energetic protons, which can exceed 100 MeV. These protons could penetrate Apollo's shielding and potentially cause damage. Fortunately, high-energy particles are far fewer in number than low-energy particles (by many orders of magnitude). Apollo also used a highspeed injection that allowed it to pass by the inner radiation belt in just a manner of minutes. Also note that the inner radiation belt is a torus (doughnut shaped) that is most intense near the center and weaker near the edges. Apollo flew inclined trajectories that bypassed the intense middle regions and grazed along the weak edges. All of this adds up to a radiation condition that was not of significant concern. Apollo passed through the region quickly and through the weak outer edges where there just weren't enough high-energy protons to cause damage.
The Orion test flight is an entirely different animal. After performing one low orbit of Earth, Orion fired its engine to alter its trajectory. The apogee was raised to 5790 km and the perigee was lowered to -29.8 km (below the surface of Earth). This orbit allowed Orion to pass through the inner Van Allen belt to test the spacecraft's radiation resistance, and then to make a high-speed reentry to test the spacecraft's thermal protection.
The inner Van Allen belt's altitude above Earth's surface ranges from about 1000 km to 6000 km. Therefore, the entire part of Orion's orbit above 1000 km was within the radiation belt. From Orion's orbital parameters, I calculate that it spent 118 minutes in this region of space. For comparison, Apollo passed through the same range of altitudes in just 17 minutes, once on the way to the Moon and once on the way back, for a total of 34 minutes. The duration of Orion's passage through the inner radiation belt was about 3.5 times longer than Apollo's.
It must also be noted that Orion's inclination was 28.8 degrees, which is lower than the inclinations used by Apollo. Orion was therefore closer to the more intense middle region of the radiation belt. More importantly, the portion of Orion's orbit above 1000 km spanned an arc of 229 degrees. This means that Orion had to pass through at least one of its nodes while within the radiation belt. The significance of this is that at some point during its passage through the radiation belt, Orion had to cross the latitudes at which the radiation belt is its most intense.
I don't have all the specific data needed to make a detailed quantitative analysis of Orion versus Apollo. However, based on the orbital data that I do have and my past experience studying the radiation belts, I think it is safe to say that Orion's radiation exposure was dozens of times greater than what Apollo was exposed to.