If you
read how unreliable the TM backups to a non-Apple NAS are (also, not supported by Apple), you'd most def want to stick to a DAS. Esp if you set your Mini up as OS X Server to provide TM service on your LAN. You'd just get a TimeCapsule with much more performance (minus the Wi-Fi router part, obviously).
Also, R/W speeds of 5D exceed those of 5N by a factor of 2 at least. Having Mini, you can run all those apps you'd cram into your NAS on a full-blown OS X plus a lot more.
Having run a NAS and a OS X Server on a Mac Mini in parallel for more than a year now, I admit that the NAS is just a waste. I'd get better performance and functionality from Mini+DAS combo. You can compare my BMST results
here. You can see, that my simple DNS-325 won't even achieve speeds that a USB 2.0 connected drive to Mac Mini does. Thus I've been looking into Drobo 5D myself. For me, only justification for a NAS is, when you don't run a dedicated server on your network.
PS could you please elaborate on the partitioning problem on a 5D and how's the 5N different?
PPS AppleTV will not connect to a network share (much like iPads and iPhones) so you either need iTunes or iOS running, reading the share and pumping the stream to aTV. Synology and QNAP users report tey can push AirPlay stream to aTV from their NASes, but you still need a browser to kick this off from NAS side. You can't browse your media lib on NAS from aTV side. Unless you run Plex on both ends.
Home Sharing service is not available to 3rd parties, because it involves authentication against Apple using your AppleID.