While discussing this argument, George Chemparathy (1983) notes the ambiguity of mahā- in the compound: is the argument based on the consensus of many people or of great people? Kei Kataoka (2011) quotes an early instance of the usage of mahājana (without parigraha) in the Mahābhārata and suggests that it only meant a ''great mass of people without a connotation of greatness in quality''. This is supported by Kumārila's contrastive usage of kaiścid eva parigraha 'agreement of a few only' in ŚV codanā 133d.
The difference with the consensus gentium of Roman law, used as an argument for the existence of God, among others, by Thomas the Aquinas, is that the agreement is still sought only from selected people, i.e. men, belonging to the three upper classes, living in India, etc. In the same passage about the agreement of few people only Kumārila ironises the Buddhists by saying ''Even they claim with respect to their own views that they are accepted by the mahājana and followed by the ancestors, taking into consideration a different continent" (TV ad 1.3.3-4). Obviously enough, such a different continent does not count.
To sum up, the consensus gentium runs more or less as follows:
Anyone, even the fool, says that God exists. Hence, he existsIn other words, the generality of the consent is the point.
The mahājanaparigraha, by contrast, in any case presupposes a selection of the kind of people involved. If many śūdras, for instance, would agree on the validity of something, this would not count as an evidence (or maybe it could even be counted as a counter-evidence). Thus, the two are radically different.
Do you find any of the two more convincing?
For other posts on Jayanta and on the way he deals with the validity of Sacred Texts, see this post.