I own both, the build quality of the HJE900 is far better. Use a hammer on them, they'll continue to work. They are the toughest phones I've ever owned.
Isolation of the RE0 is better.
Both have good sound quality. RE0 need an amp to shine imo. Overall, I think the HJE900 is superior, better timbre, bass quality, musicality whilst retaining detail. RE0 seem a touch brighter than many phones I've tried, maybe towards the Ety sound if memory serves me right. I've previously owned the Etymotic ER4P (S adapter) and the Shure SE530 and the Sleek Audio SA6 which I found were a touch too warm for my liking. The Panasonic has a better quality bass to the SA6 too. The Panasonic to my ears is a 'half way house' between the Ety sound and the Shure SE530 sound. Not bright or dark/muddy, if that makes sense. I'd say the Panasonics do indeed benefit from a decent burn in. Treble improves noticeably. Also, I took off the filters.
Lastly, I'd choose the Panasonic over the RE0 for the 'gift' factor due to the much superior packaging. It looks like a jewellery box, with a practical carry case. The RE0 case is very basic, no wow factor there.
The Panasonics are more expensive but will last a long time. If the cable was to give way, you can replace it, as the cable is replaceable, with a similar design to the Sleek Audio.
To benefit from the Panasonics, a change of tips would be required to get a good seal. The comply T400 or any double flange tip will improve the seal and isolation.
Personally, I like both phones thus far. Keepers.