Repeater and Fritz box use in my both use the same network name for both the same manual wireless channel is set. For the connected devices the two independent WLAN networks are thus virtually one and the subscriber device automatically connects to the straight receiving stronger unit.
Has had no problems in operation. Used the WLAN by 1 PC, 1 notebook, 1 netbook, 2 smartphones, 3 wireless surveillance cameras, 1 printer, 1 TV (HD streaming possible), 1 PS3, 1 ASUS Media Player, which up to the printer and all the devices access have a Synology NAS server connected via Gigabit LAN to the Fritz box.
This yet very different devices all work great with the combination FritzBox 7390 + Repeater 300E. What more do you want.
Supplement 06.01.2015:
I am still happy with my repeater function, but now changed a setting. As suggested in the comments to my review of "Lord Henry," I have now the repeater set a different wireless channel as to avoid disturbances in the wireless router itself on networks with one another. Routers and repeaters have both continued the same SSID name and the same password, but different channels. Did not measure what it really brings, but if you have enough unused wireless channels are available, so you can avoid mutual interference between the router and repeater.