With so little space having visual clues like gradient are useful. For example it may be better that you dont have a gradient on the table with check boxes but do have gradients on the wide grey + / - sections which are clickable.
The gradient gives the impression of something raised that can be clicked on whilst not taking up extra space.
You can also use shading to sharpen edges (as you are doing in your flat version anyway) and shadows to show that one section is part of another. It looks like the table of checkboxes appears when you click on the grey section - if you have a drop shadow between the grey Werkstattarbeiten section and the checkboxes below it appears like it is an extension of the heading.
Unless of course you design for Microsoft metro...