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.

To answer the question in general: yes, oven size can affect baking significantly. Jefromi's points about checking temperature, etc. are important too and more likely to cause problems.

But I just wanted to highlight two things he mentioned that are relevant specifically to oven size:

• A smaller oven means you may be forced to place your baking items closer to the walls of the oven (whether top, bottom, or sides). This is more likely to cause burning on the surface of food, sometimes while leaving the interior underdone. If this is a problem, you may need to lower the baking temperature a bit from what you would use in a large oven or try to alter the position of the food to get it as far away from heating elements and reflective surfaces as possible.

• Even baking often depends on air circulation within the oven. If you are trying to bake a large item in a small oven, hot air may sometimes get more "trapped" around any heating elements, exacerbating the problem I mentioned above.

Lastly, one other significant impact of oven size:

• Many baked goods will cook differently depending on the amount of humidity in the oven. Bread, for example, often depends on a relatively moist, steamy oven for an effective oven spring in the first few minutes of baking. Sometimes a small oven -- particularly electric ovens, which are often less vented than gas ones -- can trap the dough's own moisture more effectively, which may increase oven spring. On the other hand, too much steam can inhibit browning. (In the latter case, you may need to "vent" the oven by opening it slightly to let out steam during the browning phase of baking.)

This last point probably won't help the specific problem of burned bread mentioned in the question, but it's another issue to consider when baking in different sized ovens.