From an ATC standpoint:

At slower places, either way is usually just fine and won't really make a difference. At busier facilities (say, some of the airports around Chicago or Los Angeles), I think most controllers would prefer you file a flight plan for each leg, especially if you're going to be on the ground for a few minutes or more. We may not be able to accommodate keeping your IFR clearance active while you're on the ground if someone else wants to use the airport, so you'll need to get a new clearance anyway. The computer system tends to work better with a new flight plan for each leg, too. We can suspend your flight plan, but it's just one more thing to do that's out of the ordinary and can cause automation issues down the line.