SuttaCentral
This is two questions in one, one appropriate for Discussion, the other for the Watercooler, so I put it all there in said cooler.
Q 1: In the EBTs, does the Buddha speak of any guṇas that are uniquely his and not shared by any of his students, regardless of their realization?
Q 2: In the presently extant Theravāda tradition, are there any guṇas that a samyaksaṁbuddha has that an arhat has not?
In MN 1, in regard to various objects/aspects of experience:
The ordinary person conceives a self in relation to these objects and delights in them because they have not fully understood them.
The sekha (stream-enterer, once-returner, or non-returner) has directly known these objects and should not conceive a self in relation to them and should not delight in them because they must train further to fully understand them.
The arahant directly knows these objects and does not conceive a self in relation to them and does not delight in them because they have fully understood them and are free from greed, hatred, and delusion.
The Tathāgata also directly knows these objects and does not conceive a self in relation to them and does not delight in them because they have fully understood them to the end. They have “understood that delight is the root of suffering, and that with being as condition there is birth, and that for whatever has come to be there is ageing and death. Therefore… through the complete destruction, fading away, cessation, giving up, and relinquishing of cravings, the Tathāgata has awakened to supreme full enlightenment”.
Regarding your question, this sutta seems to indicate that the Buddha has a much deeper analytical understanding of the Dhamma (probably necessary for being able to teach it so well and adapt it so dextrously to different situations), while the arahant may have only(!) understood enough to be able to destroy greed, hatred, and delusion, thereby uprooting suffering. Of course, some arahants (like Sāriputta) may have a deep enough analytical understanding to even approach the Buddha’s understanding.