Does oven size affect baking?
First off, try and check the temperature more carefully. By far the most common reason people have trouble with their oven is that the temperature isn't what they think it is, and burning is a really good sign of that. It's very likely that when you set your oven to 350°F, it's actually hotter than that.

Ideally, you should check the temperature the bread is actually experiencing: put your oven thermometer next to bread while baking it (or an empty bread pan in that same position). The pan can disrupt the air flow, so the temperature the bread experiences might not be quite the same as the temperature in an empty oven set to the same temperature. You should also check more than once, in case it's just unreliable.

And yes, smaller ovens can exacerbate this. Baking sheets/pans will take up more of the oven, so they'll disrupt air flow more. The other thing that can happen in small ovens is getting too close to the top or bottom of the oven, so that the edges burn even if the temperature in the middle is okay.

If none of that is an issue, then I'd look elsewhere:


You might've changed something in the recipe. For example, a different pan size will result in a different baking time.
The recipes might be bad, suggesting too long a baking time, because the author's oven was too cool. Try more recipes!
You might be relying too much on time. Even if you've followed everything carefully and the recipe is good, maybe your pan is a different material that tends to bake a little faster. Be sure to check periodically for doneness.