Because I hate both of these teams with the hatred of one million suns (including the two on Tatooine), I'm not going to to a deep dive, but surface level analysis suggests Texas wins, most probably in a blowout.
1) Phil Fulmer was a guard on the Vols, and he's a loser.
2) The entire SEC was not all that good at that point in time due to its failure on the subject of integration; Texas (for all their problems integrating) had Earl Campbell, and he would have run through the Vols like hot urine through snow.
3) Tennessee's SEC record in 1970 is inflated because the three best teams not named Tennessee were LSU, Ole Miss, and Auburn - and the Vols didn't beat ANY of those teams in 1970. They lost to Auburn by 13 points at Legion Field, and they didn't have to play Archie Manning or LSU. And LSU was so good they only lost to Notre Dame - the same Irish team that beat the 1970 national champion Longhorns in the bowl game - by a score of 3-0. Texas played a much tougher schedule.
Look, whether we want to admit it or not, the SEC of 1967-1979 was - to be blunt about it - not very good overall, which is why Alabama got trashed for winning a bunch of SEC titles and going 0-8-1 in bowls until we chickened out of facing Nebraska and beat State Penn in the 1975 Sugar Bowl. From 1967 to 1975, the SEC lost almost about twice as many bowl games as they won despite going to more than any other conference (the Big 10 wouldn't allow teams to play in anything but the Rose prior to 1974). Plus, my "review of teams records vs EOY ranked teams" shows the 1970s were BY FAR the worst decade of the law of gravity (Alabama won 8 of 9 SEC titles while Ohio State and Michigan won all the Big Ten titles (sharing it five times) and OU and Nebraska won or shared it every single year from 1961 through 1988.
Note also that while Tennessee's record on integration in football is perhaps the best (early on anyway) in the SEC, it was still more of a reminder of what was wrong than what was right.
I think Texas would blow them out by three touchdowns anywhere but Neyland Stadium, and they'd blow them out by two there.
