Unless you really need full frame FX, I would get the DX Nikon D5200 or D7100 for video. You'll save some money – and these are the first DSLRs (besides the ~$3000 Canon 5D Mark III) that don't have a challenge with shot-ruining moire.
The moire from the full frame Nikons isn't as bad as the first generation Canons (or the Sonys), but it is still bad:
The D5200 is much more resistant to moire than earlier generation Nikons (please watch this comparison with the D3200 at 1080p):
Here is a wedding shot with the D7100 – cinema verite style – but it shows how challenging it can be to hold focus with a DSLR:
This one was shot with the D5200 – narative, not a wedding, but it shows the image quality this camera can produce (admittedly in a controlled setting):
There are a couple of caveats with DSLRs for event shooters – first, they stop recording after a maximum of 30 minutes and have to be restarted. So you can't put a Nikon at the back of the church and leave it running.
Second, the reflex mirror blocks the viewfinder in video mode. Outdoors, this can be a real problem, because you are forced to use the LCD for composition. So you'll have to add the expense of a loupe, EVF or external monitor.
If you do decide to go with a DSLR, my vote would be for the $697 D5200: http://www.amazon.com/gp/product/B00AXTQQDS/ref=as_li_ss_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=B00AXTQQDS&linkCode=as2&tag=videomaker22forum-20 – it is the best value for your money.
Again, hope this is helpful,