Oh. I use both fresh and canned tomatoes depending on the application.
Pasta Pomodoro-both, but usually canned
There's a sauce we do at the restaurant for our fried squash blossoms, it's one of my favorite things to make when tomatoes are really in season (Aug-Oct). Simply chop up some ripe heirloom tomatoes, run them through a food mill:
...so that you get a nice coarse puree. I heat this puree gently with a crushed clove of garlic, a big sprig of basil, salt, pepper, and really good olive oil. I don't let the puree come to a boil; as soon as I see it steam I know it's the right temp. At this temperature, the tomatoes don't develop that "cooked flavor" and keep that nice garden-y flavor, but it's still hot enough to infuse the garlic and basil. Let it steep for about 15 minutes and use this as a dip for fried zuchinni or squash blossoms stuffed with some ricotta and parmesan. You can also use it as a pasta sauce but it's a little too light in flavor for that IMO.
Ripe heirloom tomatoes are never better than simply sliced, fanned out, seasoned with sea salt, pepper, olive oil, and sprinkled with some fresh oregano and/or basil, some crumbled feta (or top quality burratta), and that's about it. I like to infuse the olive oil with a crushed garlic clove just to give it a little bite. i never ever pour vinegar or balsamic on tomatoes; it makes no sense to me to add acid to an already acidic food.
I used canned tomatoes in far too many applications to list. They're indespensible for any number of stews in almost every European country. Probably my favorite would be "Ragu Napolitano". In Naples and other southern regions of Italy they serve their "ragu" in two courses: the braising liquid and vegetables are pureed or passed through a food mill and used as a pasta sauce, and then the braised meat (something like a chuck roast, but brisket works brilliantly) is served as the second course with some more of the braising sauce.
Here's a quick method off the top of my head:
Season a large chuck or brisket roast liberally with salt and pepper. You can use any tough stewing cut here, just make sure it's in one large piece. Sear it in an appropriate sized pan in oil until it's well browned all over. The searing should be an even, gradual process that takes about half an hour. There should a dark, but not burnt residue on the bottom of the pan.
Add half a handful of sliced pancetta to the pan and let this brown. Remove the meat and pancetta from the pan and set on a platter. Add a small diced carrot, rib of celery, and a medium onion, plus 3/4 C tomato paste to the pan, turn the heat way down, and let the veg sweat, pulling up all the residue from the pan. Let everything cook for about 15 minutes, then add a small handful of dried porcini mushrooms broken up into pieces and a few chopped garlic cloves.
Add about a cup of meat broth or stock, preferably unseasoned. Make sure to scrape up any residue still on the bottom of the pot. Allow the broth to reduce all the way and form a new residue on the bottom of the pot. Add another cup of broth to deglaze, and repeat this process again, in all about 4 times. Add 3 cups of chopped canned tomatoes, another quart of meat stock, and get the meat and pancetta back in this liquid. The meat should be submerged. Bring to a gentle simmer and let this bubble gently for 3 hours. It should be fork tender. Halfway through cooking, turn the meat over.
Remove the roast and keep it in a pan tented with foil with a good amount of sauce on top. The rest of it, run through a food mill and use this is a sauce, preferably with penne or rigatoni (dry, not fresh). Grate some ricotta salata on top (don't want to use parm or pecorino here)
Serve the braised meat with some fresh vegetables. Either sauteed spinach, asparagus, or green beans would be great.
This is an all day project, but damn worth it.