As far as making the buttons stand out and look clickable compared to their surroundings, I think you've succeeded pretty well :-)
I would personally choose your side-by-side setup, especially if you're already dealing with the subject of categories and sub-categories. Your second setup risks implying the hierarchy between both. Having both options next to each other makes them equally important.
- Try to align both buttons with each other. This makes for a more balanced layout.
- Remove the borders of the Category and Sub-Category divs. Less clutter is easier on the eye. Instead, try to use a vertical separator line between both.
- Make both buttons equally wide, but edit/shorten the text in your buttons. 'New Category' and 'New Sub-Category' are pretty much self-explanatory.
- If you absolutely need to differentiate both blocks more, try adding a unique image or icon for each block.
I hope this can help you move onward with your design.