The closest one is the 3310. You'd lose a bit of power (i.e., 120 vs 130 watts per channel) and the XT version of Multi EQ Audyssey. In exchange you'd get a couple extra features (e.g., better upscaling chip, height channels, etc.).
BTW, you can still get the 3808 for under $1k, if you're willing to go refurbished. There's an Denon-authorized reseller that sells through eBay, where you can get an 8% cashback. I was able to score one from Amazon when they're clearing them out and I love it.