It will be a mirror (exactly the same as it is now, by the way).
Whatever barriers the UK puts up to FOM, the UK will see returned in kind. It's impossible to see the EU27 having it any other way.
And the UK will have to do all the running - all the EU has to do is match whatever the UK dreams up decides on.
So if the UK says EU citizens need a visa - so will UK citizens in the EU.
Work permit before you enter the UK ? Same for EU.
Only certain jobs allowed to be done by EU citizens ? Same in EU for UK.
and so on.
Yes, it will be a pissing contest. But one the UK started.
It's probably the most powerful lever in the negotiating toolbox - only the UK is in the jaws, not pulling on the handle.
The core question is politically how much are leavers going to be prepared to suffer ?
If we start with a blank slate, then it's easy to see the UK deciding you need to pay for a visa (so some going to EU) ... maybe a per-visit admin fee ????
Remember there will be a cost involved in operating a visa scheme. Somebody has to look at all applications and weed out "the bad guys" (remember this was one of Leaves biggest gripes). And I struggle to see any future government being able to defend a visa scheme which costs money - so the visa scheme will need to be self funding.
(Again, the mirror view suggests that the EU scheme would need to be self funding. I can't see EU citizens being thrilled at subsidising UK citizens).
Have no idea what criteria would be applied to weed out "bad guys".
Then we'll need a whole mechanism - IT systems and personnel - to police the visa scheme, and arrest and deport overstayers and people who abuse the visa (e.g. work when they shouldn't).
Given the UKBA is overwhelmed as we speak, it'll be interesting to see how they cope with all the additional work 
And finally the elephant in the room - the question I posed at the head of the thread. How will leavers sell the loss of prospects UK citizens are already facing ? Which is not a hypothetical now - there are a few discussions in technical areas where people have been asked if they have a non-UK EU citizenship in interviews ... which is sensible for jobs on projects that are spanning 3,4 years.
Of course, we could leave FOM exactly as it is. But it rather makes a mockery of all the pre-referendum rhetoric about "securing our borders". It's possible a post-Brexit move might be to tighten up non-EU immigration. But that doesn't square with what Theresa May was promising India yesterday (and by the way, chatting with my offshore colleagues, the view from the streets in India, is no one believes a word she says). It also didn't need Brexit to happen - the UK has always been in full control of non-EU immigration.
I did have a crazy idea (possibly the wine
) that the EU might create a stateless "EU citizenship" which UK citizens could "buy" and which would grant them - individually - FOM into the EU. This would be offered on the basis that the UK was required to allow similar "stateless EU nationals" FOM into the UK. This would be allied with a initiative to allow other EU citizens to surrender their national citizenship, and become "pure EU" citizens. But then I sort of stopped there. Although it does have a resonance in chatter from various EU countries (France and Italy) where some of the more liberal voices are expressing disquiet with their own nationality - especially where far-right extremism is extant.
It is a nice pipe dream though. 16 million Remainers paying £x,000 to Brussels (so less to spend in the UK) to keep an EU passport.
A serious question, for anyone who voted leave and is happy with the way things are going (probably a very small intersection) :
What would you be prepared to put up with reciprocally with the EU in terms of border costs/controls/visas/work permits (if we start from an assumption they're happening) ?