The Lovracelets are stuck on the boys' wrists, reflecting how they didn't get a choice to be the Battle Lovers, whereas Caerula Adamas and VEPPer have removable transformation items (rings, and then either the scarf holders or microphones), which reflects how they started out wanting to be the antagonists of their respective season.
However, the fact they're removable is actually just an illusion of that choice, as they (Kinshirou and the twins) had the seeds to be the antagonists planted when they were younger. If their items were also stuck, that lack of choice to remove them would be a hint that being Chevaliers or idols was not fully what they signed up for, and they may have fought against their respective mascot when realizing this.
On the other hand, in Happy Kiss the council's rings are stuck, just like the Happy Braces, which reflects that they did not really want to be Furanui's knights. In the very last scene, Kyoutarou and Ata shake hands, showing that neither of them have their transformation items anymore, whereas Caerula Adamas and VEPPer (presumably) retain their items after the OVA like the Battle Lovers.
Therefore, the Battle Lovers are forced to keep the source of their powers with them at all times, whereas Caerula Adamas and VEPPer have the option, and the Happy Kiss Knights and Edelstein are powerless.