I started using the food processor to make tomato puree last summer when I had tons of tomatoes from my garden, and since then I seldom use a box grater to grate tomatoes. Oh sure, if I only needed to grate a few tomatoes for a dish I probably would use a grater instead of dragging out the food processor, but these days I always have tomato puree in the freezer, so I never need to grate a small amount on the spur of the moment.
Here are five advantages to using the food processor:
1. The skins are used, not wasted. Even the tough skins of garden tomatoes blend in just fine.
2. The seeds are less noticeable because they're somewhat pulverized.
3. It's easy to make large batches to freeze.
4. It's easy to use up sudden gluts from the garden (see #3).
5. It works better than grating does if the tomatoes are rather firm.