The way I do.
I haven't tried smart object from Illustrator but if I want to use such elements from illustrator, I do following steps.

• Save as web element in Adobe Illustrator by clicking (Ctrl+Alt+Shift+S) in desired resolution or in high resolution.
• If file is saved in high resolution then resize it in Adobe Photoshop.
  Note : You must save image file without background

The way I do.
I haven't tried smart object from Illustrator but if I want to use such elements from illustrator, I do following steps.

• Save in Adobe Illustrator by clicking `Ctrl+Shift+S` in desired resolution "dpi".
• Open it in Adobe Photoshop and resize it in desired resoltion by clicking `Alt+Ctrl+I`. .
  Note : You must save image file without background