If you get offered a job you will be asigned a fleet. You may be allowed to express a preference but they will put you where they need you. 737 pilots can end up on the Airbus and 320 pilots can end up on the Beoing. There doesn't seem to be any logic to it sometimes. The 777 does a lot less long haul than the 380 and a lot more turnarounds so you will usually be home more than 8 days a calandar month, but be aware there are some long freighter trips on the Boeing fleet (and a lot of deadheading) so you could be away for up to 7 days at a time, then have 2 days off, then go away again. There will also be some rest days in there from all the night flying you will be doing, typically 3 or 4. However, when you get home at 9am after a night turnaround you will basically be sleeping most of the day. I'd say generally both fleets spend about the same amount of time in Dubai over an average month but rosters vary considerably month to month.
You may be under the impression that Emirates is a long haul airline with 3 or 4 trips away every month and a lot of time off. It isn't, it is nothing like that and the mix of flying in the Middle East is probably unique. Do not apply to Emirates thinking it will be good for your family life and you will spend lots of time at home.