It's still going to have serious issues not being outclassed by Arcanine. Not having Extremespeed, Intimidate, or Flash Fire really hurts it. Arcanine's priority kind of negates Entei's speed advantage, while Intimidate messes with Entei's bulk advantage. Entei's slightly higher attack probably isn't that important, and while the bigger HP stat helps soften recoil damage, Entei's lack of Morning Sun still leaves him overshadowed. Another thing hurting Entei in the bulk department is that it needs it's speed EV's a lot more than Arcanine, leaving less room for bulky EV's. At least with Stone Edge and base 100 speed Entei won't be getting stonewalled by Moltres and Altaria quite like Arcanine. Speaking of Arcanine, Entei would make a decent switch, eating up Extremespeed with Pressure and hitting back with Stone Edge. This seems like a good option for not being outclassed by Arcanine:
Entei @ Leftovers
Adamant Nature
252 HP / (the rest could feasibly go anywhere)
Rest
Sleep Talk
Flare Blitz
Stone Edge / Roar / Toxic
Speed EV's might work for Roar because how it works with Sleep Talk. Attack EV's would be great if you choose Stone Edge. Otherwise, defense EV's could make this a great counter to other Fire-types (Moltres might be dubious, unless it's a staller). When using Roar, Arcanine's Intimidate doesn't really mean as much in comparison, so Entei's bulk wins here. Pressure is meaningful since you have healing, and the higher HP means a lot since you are using Flare Blitz on a defensive set. This might be cool on a stall team to shuffle enemies around for entry hazard damage, while being a check to Fire type wall breakers and bulky Mismagius, both of whom can mess up stall teams. Stall teams are also likely to have spinners, which will make Entei a lot better.
Damn, I guess Lemmiwinks beat me to it :P