The game supports Cross-Save across the versions.
Settings > Application Saved Data ManagementSaved Data in System Storage → Copy to USB Storage DeviceCopyA: No. Cross-save was not supported for Battride War Genesis. You must manage save files separately for each platform. kamen rider battride war genesis save data
You might wonder, "Why not just play the game normally?" There are three primary reasons: Review: The Progression System and Save Data Architecture
When you first boot the game, you'll be greeted by Japanese prompts. To create a new save file: The Prompt: The game will ask if you want to create a save file. Select (typically the first option). Button Layout: On the PS3 and Vita versions, the Circle (O) button is usually "Confirm" and Settings > Application Saved Data Management Choose Saved