Civ 5 BNW sets the standard for civ games and I don't think civ 6 would ever be released in a long while. Furthermore, this community would have very very high expectations for civ 6, with some of those expectations already mentioned here, such as decent AI. If civ 6 is considered worse than civ 5 because it fails to meet those expectations, well I wouldn't be surprised if Firaxis coughs up a loss on that project.
However, this is what I might expect in civ 6:
1. Map design: octogons
2. Lots more luxury resources
3. Strategic resources become even more important and would also be crucial for civil purposes, like coal which is needed for factories. Also, some units may cost multiple strategic resources, so advanced aircraft would cost 1 aluminium and 1 oil.
4. Trade:
a) Trade route limit becomes dependent on tech and size of empire to buff wider empires.
b) Can set tariffs, gain more gold from trade routes from particular resources but you might suffer a diplomatic penalty.
c)Civs can offer free trade agreements to overrule tariffs. DoF's are needed though. Denounciations end free trade agreements, as does war.
d) Diplomatic resolution: World Trade Organization - tariffs become illegal.
5. Science victory is much harder again: engineer and scientist specialists would be needed to operate the spaceship. Once spaceship is built, then it is a matter of ensuring it actually enters space and the spaceship does not break apart. Think about it, if we look at the Cold War, logically speaking, Russia won the space victory because they built a spaceship first and sent it to the moon (but it broke apart) whilst America built it straight after them but it succeeded. Also, science victory would require lots of aluminium and uranium as fuel.
6. Culture victory is the same but:
a) add great playwrights and filmmakers
b) Libraries store literature, amphieatres store drama
c) Add cinema to increase happiness and store film
d) Hollywood world wonder
e) Globe Theatre stores drama
f) Great Library gives free great writer
g) Diplomatic relations also determine influence of tourism (and also the amount gained from trade routes). Strong relations offer higher tourism bonuses whilst bad relations offer tourism penalties.
7. Military rules:
a) 1UPT is improved to 2UPT, in that you can stack a melee unit and a ranged unit on the same tile, but you can't stack units of the same type, as in 2 melee units. Also, this only applies from ancient to renaissance eras.
b) archer units and city bombard only have 1 range but are more powerful. City bombard range increases to 2 once you enter modern era.
8. Domination victory remains the same.
9. Diplomatic victory would remain largely the same, but City State diplomacy becomes more diverse:
a) Add manufacturing city states (offer production to allies)
b) Personalities vary over time rather than between CS'.
c) CS' have their own ideological preference.
d) Ally and Friend thresholds also vary depending on CS personality.
10. Espionage becomes even more diverse.
11. Much better AI.
That's about it for now, but I'm sure a lot more than this is needed to civ 6 worthwhile.