I'm fairly certain a CY-1 could fit inside a 650x650mm Mk-41 cell, since it looks to be very much in the same class as VLA. I think even an S-300 could also fit into a Mk 41 given that its wings fold, so its total dimensions will not be much greater than its diameter of 500mm. Which means that HHQ-9 could fit for sure since it's smaller than an S-300.Two designs based on different doctrines of conception.
The Atago is mainly a anti-air vessel. It carries a lot of mk-41 cells thanks to their medium size. It's not a problem as anti-air missiles mainly evolve through new stages, adding length and not diameter. As such a single hull can carry as many anti-air missiles as possible.
In comparison a Type 52D carries much bigger cells and as such more capable missiles (recently we had first real images of the ship-based YJ-18 and it's gigantic in diameter~650mm at least). HHQ-9 and CY-1/5 are also quite big. These missiles can't hold in an Mk-41 cell like the one found on the Atago. Bigger cells, but it means less by Sq meters so less cells in overall. One would defines it as a multirole vessel.
In term of electronics they're very similar imo.