I bought both.
The "on" has more of a V sig and can feel a bit clamping with extended wear. Stretch them out and they feel better. V sig means mids/vocals are less pronounced so ideal for EDM (no vocals) and top 40 (whatever they're singing about, who cares, lol). They also leak sound so others can hear your music and you can somewhat hear your surroundings unless you listen at a high volume. They come with velour pads.
On the other hand, the "over" have a more balanced signature, feel more *comfortable with extended listening, and isolate better. They come with leatherette pads, and have a pivoting jack, great for ports exiting the bottom like late iPhones (whereas the "on" are straight plug which might make it difficult in a case).
Even though the "over" are considered circuma, the pads are small, say vs. HD598s that completely go around even big ears and can feel comfortable for very long sessions.
My kid uses the "on", and given the preference, I use the "over".
*Neither I would use for extended listening.
A group buy site had the "on" for $110US recently. The "over" were $199 last fall (I'm in Canada).
If you decide and go "on", I can tell you Amperiors sound better, have those too. They just don't look fancy like the Moms.