As a preliminary, let us note that building up a structure of reason from the ground need not be dogmatic. Dogmatic carries somewhat pejorative tones as resistant to reason. In a debate between an atheist and a priest, it may very well be that either the atheist or the priest or both may be dogmatic. I think the term you are searching for is foundational, as in foundationalism:

Foundationalism concerns philosophical theories of knowledge resting upon non-inferential justified belief, or some secure foundation of certainty such as a conclusion inferred from a basis of sound premises.

Second, you're in very nebulous semantics with the phrase "are equally rational" because devising a metric for rationality is no small feat. What does it mean to be reasonable or rational to begin with? Robert Audi has written The Architecture of Reason (GB) and provides a theory on the matter. And Robert Audi is but one epistemologist.

Even if two persons both have a foundational argument, there is an exhausting list on how the use of reason might differ between two parties: differences in knowledge of facts, differences in use warrant and rebuttal, linguistic sophistication, etc. What constitutes an effective rubric of rationality? That's hard to say. Whether or not an argument is easy to digest as a DAG with a root and leaf nodes is somewhat irrelevant, TBH.

*One could consider the types of logic that each party uses. If one arguer is a high school student and relies on informal logic in natural language, and the other arguer is a professional logician who can rely on formal and non-classical logics and has a detailed knowledge of fallacy and theory, then the argument could be made that whether the argument relies on regress, foundations, or circularities is somewhat orthogonal to rationality all together. The primary characteristic, then is not argument structure, but rather then use and application of inference moving from premises to conclusion.

Lastly, consider that the topic in question may have a role in regards to rationality. Is the argument over the philosophy of quantum physics in which new discoveries play an important role? Perhaps the logician in our scenario refuses to admit new evidence because of confirmation bias. Then, indeed, this dogmatism might impact an assay of rationality. Thus, a younger student might not have the same mastery of inference, but at the same time accept some important defeaters that an more conservative thinker refuses to recognize.

*Ultimately, rationality is multidimensional. So without more details, it's hard to commit to an answer to this question. It might be helpful to familiarize yourself with some contemporaneous thinking on the matter. Consider The Oxford Handbook of Rationality (GB). There are some SEP articles that might be of interest:

• Structural Rationality
• Instrumental Rationality
• Bounded Rationality

Remember, being rational is a subjective claim, because logic itself is goal driven and very subjective in its application.

As a preliminary, let us note that building up a structure of reason from the ground need not be dogmatic. Dogmatic carries somewhat pejorative tones as resistant to reason. In a debate between an atheist and a priest, it may very well be that either the atheist or the priest or both may be dogmatic. I think the term you are searching for is foundational, as in foundationalism:

Foundationalism concerns philosophical theories of knowledge resting upon non-inferential justified belief, or some secure foundation of certainty such as a conclusion inferred from a basis of sound premises.

Second, you're in very nebulous semantics with the phrase "are equally rational" because devising a metric for rationality is no small feat. What does it mean to be reasonable or rational to begin with? Robert Audi has written The Architecture of Reason (GB) and provides a theory on the matter. And Robert Audi is but one epistemologist.

Even if two persons both have a foundational argument, there is an exhausting list on how the use of reason might differ between two parties: differences in knowledge of facts, differences in use warrant and rebuttal, linguistic sophistication, etc. What constitutes an effective rubric of rationality? That's hard to say. Whether or not an argument is easy to digest as a DAG with a root and leaf nodes is somewhat irrelevant, TBH.

One could consider the types of logic that each party uses. If one arguer is a high school student and relies on informal logic in natural language, and the other arguer is a professional logician who can rely on formal and non-classical logics and has a detailed knowledge of fallacy and theory, then the argument could be made that whether the argument relies on regress, foundations, or circularities is somewhat orthogonal to rationality all together. The primary characteristic, then is not argument structure, but rather then use and application of inference moving from premises to conclusion.

Lastly, consider that the topic in question may have a role in regards to rationality. Is the argument over the philosophy of quantum physics in which new discoveries play an important role? Perhaps the logician in our scenario refuses to admit new evidence because of confirmation bias. Then, indeed, this dogmatism might impact an assay of rationality. Thus, a younger student might not have the same mastery of inference, but at the same time accept some important defeaters that an more conservative thinker refuses to recognize.

Ultimately, rationality is multidimensional. So without more details, it's hard to commit to an answer to this question. It might be helpful to familiarize yourself with some contemporaneous thinking on the matter. Consider The Oxford Handbook of Rationality (GB). There are some SEP articles that might be of interest:

• Structural Rationality
• Instrumental Rationality
• Bounded Rationality

Remember, being rational is a subjective claim, because logic itself is goal driven and very subjective in its application.