> It's a fundamentally substantive difference in the two structures

Yes, it is a substantive difference but it does not follow that this difference provides the 'constitution' property.

> one of these has an indisputable source of truth... the foundations are not the same

They are so similar as to be almost the same and if an 'indisputable source of truth' exists anywhere, it is not in the written documents or their structure but unwritten norms and rituals sit beneath both.

What stops a President from simply choosing to ignore a Supreme Court ruling and what prevents the King from returning to personal rule?

The lack of arbitrary rule is a defining feature of both and relies on something that emerged rather than something imposed from without by written words.