Personally, I'd do it with Travel City. I've heard, although I cannot guarantee it is true, that if you upgrade when you reach the desk it costs more as you have to pay extra in the form of commission (that's why the sales staff always pester you on the upgrade - because it's in their interest.)
However, sometimes you get lucky. One time we'd booked an Economy car and when we reached the desk, the member of staff asked about an upgrade (no), then told us we really needed one because of how much luggage we had (No), then virtually begged us to take one (NO!). We must have been there for 15 minutes and I couldn't work out why.
When we eventually got to our car, I worked it out. It was HUGE, a full size at LEAST (maybe higher). It seems they had run out of all the smaller size cars, so what they were trying to do was get customers to pay for larger cars via upgrading, even though if you refused they had no choice but to give you a larger car anyway!