In-game
Can't really compare them since they aren't in the same game.
Competitively
There is one format where these two were available, and that is National Dex (you can also use them in National Dex Anything Goes but both are bad there). The difference between them is rather apparent. Cinderace was very recently banned from the format due to how destructive and versatile its sets were. It could run Bulk Up and Heavy-Duty Boots, be an offensive pivot (once again with Boots), but its most dangerous set was Bulk Up Normalium Z, which destroyed common answers like Toxapex after a boost. The set was so dangerous, Pokemon like Jellicent (and even Runerigus to my knowledge?) have risen in usage in order to combat them despite them being so unspectacular against most of the other metagame threats. It was suspect tested once (in December I believe?) and it was not banned, but it was suspect tested again and it got banned literally just last week. Now yes, Protean Greninja also got banned from OR/AS OU, but that's when it didn't have any type-shifting competition (Kecleon is bad in OU). Protean has been suffering a lot because it 1. cannot switch into Cinderace (or anything, really), 2. has superior competition in Cinderace, and 3. is exploited by common defensive checks like Tapu Fini, Toxapex, and Clefable, for its Specially oriented mixed set (lacking the very rare HP Grass) and is walled by Magearna, Mega Scizor, and Toxapex on its Choice Scarf set and Physically oriented mixed set. With Cinderace out of the way, Protean Greninja should be able to start picking up some usage. As for Ash-Greninja, it is one of the best Special Attackers in National Dex, with an incredible Speed stat, a huge Special Attack stat, and a great offensive typing. Hydro Pump has few resists and massive power, especially with Choice Specs. Meanwhile, Dark Pulse slams most things Hydro does not hit as hard, such as Serperior, Ferrothorn, and Toxapex. It also has great priority (after evolving into Ash-Greninja) in Water Shuriken that demolishes the most common Choice Scarfer in Landorus-Therian, and it also has access to Spikes to wear down its checks and support its team, as something like Heatran switches in fear of its Attacks. Protean also has Spikes, but can't take advantage of them as well as Ash-G can.
Now, for the usage stats, you can see that Libero Cinderace is used on around 12% of National Dex teams, while Protean Greninja is used on around 4.3%. Ash-Greninja has more usage than Cinderace, sitting at 13.92%, but usage doesn't mean broken, as shown with Landorus-Therian having more usage than Spectrier and Urshifu-S in OU before they were banned.
