Parks & Recreation is one of the best sitcoms of the last 10 years, and part of its quality comes from the fact that it was basically a live-action version of The Simpsons. That's not to say Parks & Recreation didn't have its own sense of identity, but a lot of its humor and characters were quite clearly inspired by the animated classic.
Parks & Rec was born out of the same creative team as The Office, and was almost a spin-off of that show. That DNA is clear in season 1 in particular, where the show stayed too close to what had made The Office work rather than focusing on what it could be. It was only from season 2 and beyond, when they realized that Leslie Knope shouldn't just be another Michael Scott, that Parks & Rec truly started to flourish.
Across all seven seasons, the adventures of the Parks & Rec team took place in the fictional town of Pawnee, Indiana, and that's where the comparisons really begin to set in. Leslie may not have much in common with Homer Simpson, but Pawnee is essentially like Springfield, only live-action. One of the hallmarks of The Simpsons isn't the family itself, but the varied cast of supporting and minor characters who constantly recur throughout the series. They're what make Springfield feel like such a lived-in place, and provide a number of sources of humor.
While many sitcoms have been influenced by The Simpsons, it's hard to think of any other live-action comedy that has so successfully adopted this same approach to its setting. From Ken Hotate to Joan Calamezzo, and Mona-Lisa Saperstein to Jean Ralphio, Parks & Rec's Pawnee, Indiana, is filled with a colorful (and often just bizarre) cast of characters who feel like they can pop up at any given moment. They might go multiple episodes or even seasons without an appearance, but you know they're always there and could return.
These characters serve the larger plot, but also have their own functions: to appear, say a few lines (maybe a catchphrase), and generate some big laughs, while relying on the sense of familiarity that increases with each appearance. Some feel like they've been directly inspired by The Simpsons, such as Perd Hapley being Pawnee's version of Kent Brockman, The Simpsons' Mayor Quimby becoming Parks & Rec's Councillor Dexhart, or even the fact that both towns have a bitter, superior rival, with Eagleton being the Shelbyville to Pawnee's Springfield.
Whether they're exact matches or not, it's clear (and great) to see The Simpsons' influence all over Parks & Rec's approach to its setting, which in many ways becomes a character itself, given its importance to the show as a whole. Greg Daniels, co-creator of Parks & Recreation, worked on The Simpsons during the 1990s, so it's perhaps no surprise that it can be felt so readily in Parks & Rec.
There are elements of Lisa Simpson in Leslie, or of Homer in Andy Dwyer, which further add to Parks & Rec being like The Simpsons. But it's mostly in the way it uses that all-important supporting and minor cast of characters to bring its town to such vibrant, weird, and hilarious life that it feels like a live-action The Simpsons. Springfield and its characters are what helped The Simpsons stand apart in the animated crowd long before the likes of Family Guy came along, and it's what has helped make Parks & Recreation such a unique live-action sitcom too.