Of course there's a noticeable difference. The Accord is a larger, heavier car with a larger engine. That one is also 17 years old so it may do even worse depending on condition. The EPA ratings, while not always real-world accurate, are pretty decent for comparison purposes.

And remember these MPG ratings and numbers are from ideal testing situations so without a doubt you'll already be getting a lower MPG in real world conditions. Not a huge difference but it's already going to be lower. And adding to it the car being old and I'm assuming a lot of city driving with your job.

There will be a significant difference in fuel consumption. The Accord is a V6, and the Civic is a 4-cylinder. That means you're going to be burning roughly 50% more fuel for the same idle speed. It's not quite that high in reality, as larger engines can idle at a lower RPM. Still, you're inevitably going to get roughly 33% less mileage. Add in the fact that the engine is hauling a heavier car just adds to being fuel inefficient. More cylinders=greater fuel consumption. 

When gas shot up to $5.05 a gallon, I tried to beat EPA-estimated highway mileage, as most of my commute was on the highway. I was driving a 1999 Ranger 4x4 with a 3.0L Vulcan V6. The truck gets 19 MPG highway per the EPA, and I managed to get 22.5 MPG once. I would go 60 MPH in the right lane, and I'd cruise with the RPMs sitting around 2100. Accelerating and slowing down uses the most gas, by far, so I tried to time traffic lights and coast As much as possible. I got really good at it. The truck has almost 300k miles on it, too.

Being an Uber driver, you will stop and start like no tomorrow, most likely. You can't take advantage of the highway like could, so you will inevitably get less gas mileage.