Presumably the question is referring to temperature gradients within the egg, i.e. the difference in temperature between the outside and inside. That is actually pretty relevant cooking-wise, because it tells you how the yolk and white will be cooked.
tl;dr I'd expect to see a steeper gradient from boiling than from the convection oven, but the actual results from your lab will let you tell much more confidently.
This depends on how fast the heat transfer is, which is made most obvious by the temperature the shell is held at. You can also see it from total cooking time. If one method takes longer, then it's transferring heat more slowly, and thus you can expect a flatter temperature gradient inside the egg (there's time for the heat to propagate inward), while the faster one will have a steeper gradient (the outside heats much faster than the heat propagates in).
With boiling, there's really only one possibility: the water holds the shell at very close to 100C. You have very efficient heat transfer, the water is well-mixed, and it has a very high heat capacity, so it can easily do this. Hard-boiling eggs generally takes less than ten minutes.
With an oven, it's less clear. Without any convection, the shell will actually remain well below the oven's air temperature for quite a long time, because the air can't transfer heat rapidly enough. This is likely true even with a realistic convection oven: if you put the egg in, wait a minute, and then check the shell temperature, I highly doubt it will be at the oven air temperature. Baking without convection in the 350F ballpark generally takes around half an hour, and I believe convection only reduces that to 20-25 minutes. So I'm pretty sure the oven has less efficient heat transfer, longer cooking time, and flatter gradient, but if you had a powerful, hot enough oven with really good convection, that could flip around.
So overall, it's hard to say for sure just from your description. If you actually did an experiment, though, you can tell from the results. Egg whites are soft but solid at 155F, and totally set at 180F, while egg yolks are firm at 158F and dry/crumbly at 180F. A steeper temperature gradient within the egg means that the yolk will be less cooked compared to the white, while a flatter temperature gradient means that they'll be cooked more similarly.
If you noticed differences in cooking time, or differences in yolk vs white doneness, there you are.
All this said, dry vs wet heat does have other significant effects. Dry heat will dry out the membrane and even some of the white underneath. Given enough time, the white will shrink away from the shell and end up noticeably drier and tougher, and it can even brown. So the differences you notice in the resulting egg may not be only about temperature gradient.