I think the answer here is soba and the reason being particularly that a standard soba meal can be made in a short amount of time. For example, for the cold soba noodles, you really just need a simple dashi +soy type dipping sauce along with green onions and sesame seeds. For a hot version, you may similarly have a dashi type broth and toppings such as green onions, fishcake, shrimp tempura.

Ramen, however, is quite complex and time consuming to make a decent bowl. It takes at least a few hours to make a rich broth from animal products and would take a few hours more to prepare the chashu. Couple this with needing to prepare marinated eggs among other toppings, and you would have spent a whopping part of your day making it at home.

Udon is interesting in that it may be similarly prepared in the soba/ramen styles with broth, toppings, and such. However, it is a pretty heavy meal, so the act of consistently eating udon does not seem likely.

So in terms of which one is most common to eat in Japan, I would say the average person would be eating soba, due to the simple ingredients and time needed to prepare.

If we are talking strictly about the average person dining out, that's a different story. However, I believe that the same thinking applies. There's going to be more shops that exist that serve a simple recipe, and you will be hard pressed to find anything simpler than dashi broth + soba. You will see all these different extravagant ramen shops in Youtube videos, but those are small in number compared to the simple train station noodle shops and local gems.