On the mobile front, NFS: No Limits is dueling against the Asphalt series, particularly the eighth and ninth installments, a game that plays similarly to the console and PC versions of NFS.
Need for Speed 2015 would later take on Forza's vinyl/wrap editing capabilities, with design sharing later added in the Showcase Update.
Forza is also a competitor to the second era of the NFS games, due to " Design-It-Yourself Equipment" abilities like vinyl editors and performance upgrades.
And as noted above, Test Drive Unlimited will be rejoining the open-world racing game competition after a decade-long Sequel Gap. In addition to those two games, Ubisoft's The Crew games have joined the fray with their massive open world and ability to customize vehicles. GT has actually been the strongest competitor to NFS for years despite being a semi-sim PlayStation first-party exclusive and not a usually-arcade-like racer on multiple platforms like NFS, while Forza on the Xbox has been using the Horizon series to go after the Wide-Open Sandbox aspect of more recent racing games to target NFS among others, even though it too is a semi-sim series.
Finally today, it's mainly Gran Turismo and Forza.
note An interesting situation happened with Midnight Club, as the Complete Edition of Los Angeles would end up being the game's last release before going on an indefinite hiatus as its publisher, Rockstar Games, focused on their Grand Theft Auto franchise, meaning that Midnight Club more or less "forfeited" this duel. It would take the third era's Shift subseries and a revival of the Hot Pursuit name to get out of that funk.
The second era of NFS actually saw two different parts having different competitors during the first part it was Juiced and Street Racing Syndicate, Underground trounced them both and during the second part of the same era, during which NFS took dips in quality, it was being beaten by other games like Midnight Club: Los Angeles and EA's own Burnout Paradise.
Test Drive fell off by the wayside and had a reboot with Test Drive Unlimited, but that series was eventually defeated by EA's series, although a third TDU is in development for a planned 2023 release.
During the late 90s and early 2000s, it was Test Drive.