Provided the SSPX priest was ordained by one of the Society bishops, the biggest difference is that the SSPX Mass is said by an undoubtedly valid Catholic priest while the indult/diocesan Mass is said by a priest whose orders are, at best, doubtful because he was ordained in the new rite by a bishop who was likely consecrated in the new rite.
Thus, with the SSPX traditional Mass, you have the sacrifice of Calvary, the body and blood, soul and divinity of Christ.
With the indult/diocesan traditional Mass, you have a layman at the altar pretending to be a priest and you have a very nice Last Supper re-enactment and you end up with bread and wine.