Convenience vs ibuprofen is a thing given the longer half life, but it still generally comes with similar risks. If you are taking anything for more than just an occasional headache, definitely discuss with a doctor, COX2 selectives like celecoxib may be a better risk profile and even more convenient.
(COX1 and COX2 selectivity loosely separate which systems get the brunt of the side effects)
There are also slow release forms of naproxen. (Which make sense given its long action: lets people fade in the next one while the previous dose slowly fades out). That could also help make it easier on the GI tract.
Unless I am missing something, the data really doesn't back that up. naproxen is much more longer lasting and has a higher chance of causing ulcers. Hence why its not over the counter in the UK and is prescribed with omeprazole to reduce the risk of issues.
Naproxen will be around longer due to its long half-life, so it creates more opportunity for this problem.