If you exclude XBMC, Redmine and Music Server, I have already done those (with the addition of a PostgreSQL database and Mozilla Firefox SyncServer) and I can tell you it works very well with 256MB RAM (240MB since the memory split won't take less than 16 for the GPU). Of course there is no desktop UI. It took me about a month or so, playing around in my free time..
To play movies you'll need at least 64MB RAM for the GPU, and the XBMC is very resource hungry (in all CPU-RAM and I/O ops) so it won't leave space for anything else in your 256MB so it won't fit. It's one or the other, you can't have both.
You can use one Raspberry for all the server stuff (mail, webserver, cloud, NAS etc) and one more for the media stuff (XBMC mostly, maybe MPD as well).
You may also need a powered USB hub for external hard drives or other peripherals, so consider this cost as well.
An important note is that the poor ARMv6 and the humble bus of the Pi cannot compete with the multicore x64 all-in-one server in performance. Also, it will require significantly more time to have everything up and running and tweak the configs to get the best of it (unless you consider this a hobby, so it's fun :) ).
Conclusion, attempting to answer the question. The all-in-one server will perform much better in all aspects, even compared to a team of 4-5 RasPis. The Pis are more fun and can do all the work but will be slower as much as they are cheaper.