What are your Illustrator > Preferences > File Handling … settings?
The EPS-Setting ist off and the clipboard options are both on (PDF and AICB). The "keep path" -selection is selceted.
What version of windows are you using?
Do you mean in photoshop, if you use Edit>Paste, you don't get a dialog, but it just pastes as a vector smart object?
Are you actually using copy and paste or dragging the shape from illustrator to photoshop?
Is this something you created in illustrator or an pixel based document you placed into illustrator and worked on?
As R. Kelly said, if it's based on pixel artwork and you e.g. created a clipping mask, the behavior would be normal. Only released paths can be inserted as shape layers. Other than that you might check the appearnce of the object in Illustrator. Certain effects and tools cause flattening and then likewise, pixel data for them is produced that can only be inserted as an SO.
I can't tell why, but today everything works as it should. I didn't change anything at all. Yesterday a restart of both programs didn't help. Maybe a restart of the windwos system was needed.
Thank you all for your responses.