I've not heard the Sennheiser HD650 or the 660s but I have heard the new HD599s which are supposed to be up there with the long standing legendary HD600.
In a straight comparison I found the HiFiMAN 400se to be considerably more life-like than the HD 599.
If funds allow then the HiFiMAN Sundara is probably as good a headphone as anyone will ever need and should be on your list.
I've listened to the HD599s and the 400s through a dedicated headphone amp and through the headphone jack on my Xiaomi phone.
With well recorded music (Lambchop, Diana Krall Live) through the headphone amp the HiFiMAN 400s were easily better than the Sennheisers.
With less well recorded music (Cat Steven' s Mona Bone Jakon and Bowie's Reality etc) through the headphone amp the gap narrowed considerably but was still perceptible.
Through the smartphone alone, the gap had more or less disappeared.
The first conclusion I drew was that the smartphone couldn't optimally drive the HiFiMAN phones to demonstrate their superiority.
The second conclusion (more or less a given with any audiophile comparison, as anyone who's been to a show will appreciate) was that it's only with high quality recordings that sonic differences become more apparent.