I had this problem streaming from my iPad to Apple TV via a Linksys WAG160Nv2 router. Worked fine when the Apple TV was connected to the router by WiFi, but not at all when connected by Ethernet.
The problem was resolved by disabling Internet Access Priority (aka QOS) on the router.
Before I tried this, I got some slight improvements in behaviour by disabling SPI Firewall Protection and the option to Block Anonymous Internet Requests, but neither of these tweaks were required once I disabled QOS.
It does seem odd that these apparently WAN-related options affect the internal bridging between Ethernet and WiFi, but that's what seems to be happening.