Payton is a nobrainer IMO.
He WAS the offense
QBs he played with: Bob Avellini, Bobby Douglass, Gary Huff, Virgil Carter, Vince Evans, Mike Phipps, Jim McMahon, Steve Fuller, Greg Landry, Rusty Lisch, Mike Tomczak, Doug Flutie, Jim Harbaugh. Heck, Payton himself lined up at QB a few times. Basically, Jim McMahon was the best he played with. That's not saying much.
Payton played with 1 Pro Bowl QB in 13 seasons: McMahon in 1985. (And why exactly did McMahon make the Pro Bowl? The Bears passing offense was 22nd in yards and 23rd in TDs... McMahon threw for 2392 yards and 15 TDs.

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Not only did he never play with a 1000 yard receiver, he never even played with a 900 yard receiver. In fact, only 3 times in his 13 year career did any Bears receiver top 800 yards, and only 3 other times did any Bears receiver top 700 yards. And there were no good receiving TEs, either. It should come as no surprise that no Bears WR (or TE) made the Pro Bowl during Payton's career.
To reinforce this, consider Chicago's pass yardage ranks during Payton's career: 23 (of 26), 28 (of 28), 21, 26, 26, 28, 28, 22, 17, 26, 22, 24, 14. They finished in the bottom quarter of the league 10 times in Payton's career.
Payton himself led the Bears in receptions 6 times, and had the second highest total 5 other times.
In his last few years, his offensive lines were pretty good, but for most of his career it wasn't. Two of Payton's linemen made the Pro Bowl a total of 5 times in his 13 seasons, all in his final 3 seasons: Jim Covert (1985, 1986), and Jay Hilgenberg (1985, 1986, 1987).
Compared to Jim Brown
Brown is the only back I would consider comparing to Payton, and I admit I didn't see him play, so that may bias my opinion. That said, consider that Brown joined a dynasty.
1950-56 (pre-Brown): 63-20-1 (.759), 6 postseason appearances in 7 years, 6 championship games, 3 championships
1957-1965 (with Brown): 79-34-5 (.699), 5 postseason appearances in 9 years, 3 championship games, 1 championship
Now compare that to Payton and the Bears:
1968-1974 (pre-Payton): 31-66-1 (.320), no postseason appearances
1975-1987 (with Payton): 111-83 (.572), 6 postseason appearances, 1 championship
How about a supporting cast comparison? Payton's is addressed above. It seems very hard to support the notion that the Browns were not already a very, very good team when Brown joined them, which naturally implies that he was surrounded by a talented group of teammates. Remember, there was no free agency (or draft?) at that time, so it would be very hard for me to see how the talent level of a team that appeared in 6 championship games in the 7 years prior to Brown's rookie season had suddenly dropped to average or worse. This is supported by the number of Pro Bowlers Brown played with:
- Browns QBs made the Pro Bowl 4 times in Brown's 9 seasons: Milt Plum (1960, 1961), Frank Ryan (1964, 1965).
- Browns WRs made the Pro Bowl 5 times in Brown's 9 seasons: Ray Renfro (1957, 1960), Bobby Mitchell (1960), Paul Warfield (1964), and Gary Collins (1965).
- Brown played with the following Pro Bowl offensive linemen: Art Hunter (1959), Mike McCormack (1957, 1960, 1961, 1962), Jim Smith (1958, 1959, 1960, 1961, 1962), John Morrow (1961, 1963), **** Schafrath (1963), Gene Hickerson (1965), John Wooten (1965). That's 7 different linemen for a total of 15 times in 9 seasons, and only one season without a Pro Bowler--1964. In 6 of his seasons, Brown had 2 or more Pro Bowlers on the line.
To be fair, there were fewer teams when Brown played, so it stands to reason he would have played with more Pro Bowlers. Still, the difference is too big to be accounted for simply by that IMO.
I just don't see evidence that Brown was better. Again, I admit that could be because I never saw him play with my own eyes, while I did see Payton play often.
Conclusion
Payton's accomplishments are more impressive than Jim Brown's (or any other RB's), IMO.