Loud enough to need a headset for sure, noise cancelling type.
Given that any Ez is capable of long flights, an ANR system is very desirable to reduce/remove the noise factor from the fatigue equation.
Although I fly a VEZ, I'm sure that the noise level is comparable to the LEZ. I definitely agree with both of the above comments. I have and really like my ANR headset. Noise levels are qualitatively the same as spam can levels. You also need an intercom with headsets to have an acceptable passenger situation.
The primary source is prop noise through the relatively thin canopy, I believe. The high cruise speeds of EZs also can make "wind noise" more of a problem if you don't have good air-leak sealing around, for example, the canopy. In summary, don't plan on "whisper quiet" with the engine in the back, nor the really high levels of noise that you can get in helicopters or open cockpit. Intercoms and headsets that work in a spam can will also work in an EZ - but keep in mind that electrical shielding can be more of a problem in a composite without all that tin in the airframe to soak up stray RF. IMHO, quality headsets and intercom systems are good investment.
