Ibuprophen and Naproxen are very similar when it comes to providing relief from inflammation and as to their analgesic properties. Both have minor inhibitory effects on bone healing.
My son's specialist recommended the Aleve the first time around and then the Ibuprophen the second time around after diagnosing different nerve problems. It was more an issue of dosage vs. availability to take the NSAID than a preference for one over the other. Both worked but then eventually after we weaned him off the NSAIDs a problem with forearm pain returned. He was seeing a doctor who is also a nerve specialist for an unrelated bone injury and he said that there wasn't and hadn't been a nerve injury. The two doctors are colleagues at Kerlan-Jobe. The MRI showed synovial plica to be a potential problem although there wasn't a "smoking gun" at the location of the pain. This doctor prescribed the Medrol dose pack which is an oral corticosteroid similar in it's effects to cortisone. It knocked out the inflammation within a couple days whereas it had taken months with the Naproxen. We waited a week after finishing the dose pack before starting him on an interval throwing program to make sure there wouldn't be any masking issues. They call it a dose pack because you take it on a strict schedule building up and then tapering down the number of doses taken each day. I'm not a doctor but I don't think the Medrol would be appropriate for anything significantly post-surgery or injury.
As long as your son doesn't have a tendency toward stress fractures then there should be no issue with the Naproxen on that account. However, you do need to keep an eye on the liver with any NSAID if taken in theraputic doses over a long time period.
We are much more careful these days to avoid letting any inflammation take hold. He ices and will take some NSAIDs after a heavy throwing workout, but he doesn't take NSAIDs on a regular basis.