There are many reasons that the San Antonio Spurs are the best franchise in the modern NBA world.
1. Consistency: No other NBA team has been able to have a winning record and make the playoffs 21 straight years going
2. Hall of Famers: Tim Duncan, David Robinson, Tony Parker, Manu Ginobili. No doubt future hall of famers San Antonio has produced. Other possible future candidates include Bruce Bowen, Kawhi Leonard, Etc.
3. The winningest trio of all time in the Spurs big three.
4. Gregg Popovich is probably the greatest coach ever to touch a playbook. The Golden State Warriors have adopted former Spurs player, And Spurs assistant coach Steve Kerr and he has implemented much of the Spurs playbook. Almost every team in the NBA consistently runs a play that was invented by 'Pop'
5. Championships: 5 Championships in 17 years. Only the Lakers have had that success in 90's and 2000's basketball. (The Lakers failed past 6 years take away from there chance to be the dynasty
6. Somehow after the events of the 2018 offseason, They still keep winning. Go Spurs Go!
The Golden State Warriors would have to take that from the San Antonio Spurs. The Golden State Warriors have 3 championships (Most likely 4 after this season) already and show no signs of stopping. In addition to this the Golden State Warriors have the best lineup of all time with 1. Stephen Curry, 2. Klay Thompson, 3. Kevin Durant, 4. Draymond Green, 5. DeMarcus Cousins. Overall the Golden State Warriors are likely to surpass the achievements of the San Antonio Spurs and there is also much more time in the 21st century to jump to conclusions.
As a Spurs fan myself I would say that the San Antonio Spurs are one of the best franchises of NBA history. Even though Spurs won 5 times, They never won a back-to-back (which is a big thing in any sports). The Golden State Warriors, Los Angeles Lakers and the Miami Heat teams were a dynasty at some point, Which Spurs couldn't quite count as a dynasty because of the reason.