Several points here:
- The NCAA recognizes no National Champion in I-A football. PERIOD. They list some things on their website just for fun. So they are all Mythical National Championships (MNC).
- Most of the things you see listed on the NCAA website or elsewhere are computer ratings or other systematic formulas, NOT polls. Most of them do not actually award championships and most of them were not contemporaneous.
- The first contemporaneous "national champion" as far as I have been able to determine was the Dickinson System, a statistics-based formula devised by a U of Illinois professor, who awarded national championships from 1926-1940. This is not a widely accepted MNC.
- Prior to about 1936, there were no real national champions. 2 things happened in 1936: The AP Poll started ranking teams and handing out a trophy, and the Helms Athletic Foundation started a panel of experts to select the national champion.
- Helms also went back and retroactively examined previous football seasons to 1901 and named national champs for those years as well. Since then, others have retroactively named champions as well, such as the National Championship Foundation and Billingsley (a power rating formula). None of these were contemporaneous!
- Prior to 1936, there was something kind of like the BCS, called the Rose Bowl. The idea of the Rose Bowl was to pit the best team from the East against the best team from the West. The winner was not called the national champion, but it's hard for me to argue against the MNC for a team that won the Rose Bowl and had the best record.
- The AP poll and the Coaches' poll are the two universally recognized sources for national champions. The coaches poll started in 1950 as the United Press (UP) poll. Another news organization called International News Service (INS) did a poll of writers and coaches from 1952-1957, but this was merged with the UP poll when UP and INS merged to form United Press International (UPI) in 1958. Yet another poll started in this era is the FWAA (Football Writer's Association of America) beginning in 1954.
Now given this background info, we can look at GT and UGA's MNCs:
1990
Colorado: AP, Berryman, DeVold, FACT*, FB News, Football Research, FW, Matthews, National Championship Foundation*, NFF, Sporting News, USA/CNN
Georgia Tech: Dunkel, FACT*, National Championship Foundation*, UPI
Miami (Fla.): Billingsley, Eck, FACT*, NY Times, Sagarin
Washington: FACT*
GT won the coaches poll, LEGIT.
1980
Florida St.: FACT*
Georgia: AP, Berryman, FACT*, FB News, FW, Helms, National Championship Foundation, NFF, Poling, Sporting News, UPI
Nebraska: FACT*, Sagarin
Oklahoma: Billingsley, Dunkel, Matthews
Pittsburgh: DeVold, FACT*, Football Research, NY Times
Georgia won the AP and coaches' polls, LEGIT.
1968
Georgia: Litkenhous
Ohio St.: AP, Berryman, Billingsley, Dunkel, FACT, FB News, Football Research, FW, Helms, National Championship Foundation, NFF, Poling, UPI
Texas: DeVold, Matthews, Sagarin
Georgia won a rinky-dink rating system with an 8-1-2 record, Ohio State was 10-0 and won both polls, BOGUS.
1956
Georgia Tech: Berryman
Iowa: Football Research
Oklahoma: AP, Billingsley, Boand, DeVold, Dunkel, FW, Helms, INS, Litkenhous, National Championship Foundation, Sagarin, UPI, Williamson
Tennessee: Sagarin
Georgia Tech won a rinky-dink rating system with a 10-1 record, Oklahoma was 10-0 and won both polls, BOGUS.
1952
Georgia Tech: Berryman, INS, Poling
Michigan St.: AP, Billingsley, Boand, DeVold, Dunkel, Football Research, Helms, Litkenhous, National Championship Foundation, Sagarin, UPI, Williamson
Georgia Tech was 12-0 and won a recognized media poll (INS), Michigan State 9-0 and won the other polls, LEGIT.
1951
Georgia Tech: Berryman, Boand*
Illinois: Boand*
Maryland: DeVold, Dunkel, Football Research, National Championship Foundation, Sagarin
Michigan St.: Billingsley, Helms, Poling
Tennessee: AP, Litkenhous, UPI, Williamson
Georgia Tech finished 11-0-1, won a couple of rating systems. Tennessee won the polls (which were pre-bowl at that time) but lost to 10-0 Maryland in the Orange Bowl. BOGUS, although from a retrospective point of view, better claim than Tennessee.
1946
Army: Boand*, Football Research, Helms*, Houlgate, Poling*
Georgia: Williamson
Notre Dame: AP, Berryman, Billingsley, Boand*, DeVold, Dunkel, Helms*, Litkenhous, National Championship Foundation, Poling*, Sagarin
Army had not lost a game in 3 years and Notre Dame fought them to a 0-0 tie, both teams finished unbeaten with a tie and between them shared MNC honors. Georgia finished 11-0 and won a rinky-dink rating system. BOGUS.
1942
Georgia: Berryman, DeVold, Houlgate, Litkenhous, Poling, Williamson
Ohio St.: AP, Billingsley, Boand, Dunkel, Football Research, National Championship Foundation
Wisconsin: Helms
Georgia finished 11-1 and beat UCLA in the Rose Bowl. Ohio State finished 9-1. Georgia's loss was 27-13 to a mediocre 6-4-1 Auburn team, while Ohio State lost to a strong 8-1-1 Wisconsin team picked as national champs by one source. Still, Rose Bowl win = LEGIT.
1928
Detroit: Parke Davis*
Georgia Tech: Billingsley, Boand, Football Research, Helms, Houlgate, National Championship Foundation, Parke Davis*, Poling
Southern California: Dickinson
Georgia Tech was 10-0 and beat California in the Rose Bowl. USC tied California and finished 9-0-1. LEGIT.
1927
Georgia: Boand, Poling
Illinois: Billingsley, Dickinson, Helms, National Championship Foundation, Parke Davis
Notre Dame: Houlgate
Yale: Football Research
Georgia finished 9-1 and won a couple of rating systems, lost the last game of the season 12-0 to 8-1-1 Georgia Tech. Illinois finished 7-0-1 with a tie against mediocre 4-3-1 Iowa State. BOGUS.
1917
Georgia Tech: Billingsley, Helms, Houlgate, National Championship Foundation
GT finished 9-0, outscored opposition 491-17, and had not lost a game in 3 years. LEGIT.
So there you have it: 4 LEGIT MNCs for GT and 2 LEGIT MNCs for UGAg.
You could argue more or less for either team, but those are recognized by the historical consensus.