Pre-Aegon, who out of the Tullys and Tyrells would have had more prestige respect and power. I’m thinking the Tullys because what they had was theirs, they had land, a castle, they were a very old house dating back longer than the Tyrells. But would the Tyrells connection and marriage into the Gardeners elevate them in anyway?

House Tully would probably have more prestige, because they were an ancient house and had their own lands and title.

But House Tyrell definitely had more power. As High Stewards of the Reach, they were the right-hand men to the Gardener Kings, and exercised enormous influence over the kingdom. While Tyrells were Regents of the Reach during the minority of Garland VI, I think the more instructive example was Ser Osmund Tyrell. Following the death of Garth X and the Manderly-Peake civil war, Ser Osmund got 40 houses to follow his lead, put down the Manderlys and the Peakes, and chose the next King of the Reach. 

So even before the Field of Fire, the Tyrells had become the power behind the throne.