The key difference is that there is no focused distribution of Raw Production.  Research, Wealth, Construction, etc, all use the base Raw Production number and apply their separate bonuses to the same value.  It the planet gets 2 production, then each category gets 2 production to work with.  There is no trade off you can engineer between those categories, which was the prime driver for planet specialization.

For purposes of adjacency accumulation, planet specialization still matters.  Adjacency bonuses aren't very big, but if you keep adding them up, it is one of ways you can boost your overall output.  Since there is no production trade off, I have found that I can specialize according to some terrain suggested goal, like research, but still put a market on that isolated +3 Wealth space.  I don't see that I really lose anything doing that.  The only time that might not apply is if you have some hub improvement you are using that gives a flat bonus.  In that case, you want to specialize that planet to maximize the percentage bonuses applied to that flat value.  Central Bank is an example of a flat bonus you would want to specialize for.  If you don't have any flat bonuses involved, it seems like you could even run the planet to terrain bonuses while ignoring any colonizing event bonuses.  Both will still get applied to the same production amount.  But in the end, adjacencies are your main planet empowering tool and the main driver for planet specialization as far as I can tell.

For purposes of function, it still helps to create Ship Manufacturing power houses.  It is easy to research ships you can't afford to build quickly.  All too easy.  Watch out, it's a trap  So a high manufacturing planet or two or three supporting a Shipyard is a very good idea.  It doesn't take Ship Construction improvements to get this.  The Space Elevator and the Factories do a lot. But for a dedicated Ship building planet, the Ship Construction improvements can be a specialization you would want, especially if you have any fleet-wide bonus improvements to use.  

After allowing for that, or while I am looking for special case planets, I build mostly-Research or mostly-Wealth planets as needed to keep my economy growing.  I have to watch that I don't overemphasize Research.  My wealth is always relatively slow to build, but I am working on that by making sure I have enough Wealth or Mostly-Wealth planets.  I may also put a little more manufacturing improvements than a truly specialized approach would call for.  I have shipyards everywhere, and I always feel my planets are upgrading too slowly, so that breaks up some of the more extreme specialization patterns.

I am exploring the idea of a Farm planet.  It looks like it is very effective.  Put all the farms you can in one place and go for it.  Then I think I am looking at putting a City and a Hospital on all the other planets.  It may be something for a mid-game move as opposed to initial implementation.  I am thinking a Farm and a City on each planet until I build up the Farm planet. Then I will switch all the individual planet Farms to Hospitals to fill the City.  Right now, I don't see a need for a second City.  Or a second Farm Planet.  With a bunch of adjacencies going, that Farm Planet can put out an awful lot of food, even enough for my sprawling empires.  Impressive.  And I haven't even gotten into Food Distribution techs yet.  I wish there was some sort of growth bonus for having excessive food levels.  

You can create a culture specialized planet for individual border growth or intentionally flipping a neighbor, but the influence mechanism has been slowed significantly, so I haven't tried that yet.

All this is from the viewpoint of very large maps with lots of room to grow.  Crowded maps will introduce complications depending on how many planets you get and what they are.  Other factions provide interference to the best plans.  This is likely to emphasize the trend towards specialization by function, especially if you are dealing with very few planets to work with.  I think people are crazy for playing on crowded maps, so I won't even try to discuss that scenario further.

Good luck!  And if you figure out anything further yourself, let us know!

Well, the downside to that is if you get pegged with a spy or the planet gets invaded.

There's really only one scenario where it would actually be bad for a planet to be "specialized" in that there are galactic wonders you can use to radically boost your unique leveled flats.

If you get this perfect planet that just begs to be one huge wheel of awesome, with loads of tiles grouped together, some strategically located bonuses, and a large number of asteroids around it, you can create one giant production power house centered around the Antimatter Power Plant.  You group the various capitals and other high level boosts around the leveled flats that have been placed next to that fantastic +5 centerpiece, hopefully with one or two further advantaged tiles, and load the planet up with gobs of citizens giving their multiplier to your sky high 30+ raw production planet with leveled flats doing another 10+ to each category.  It's entirely reasonable to end up with a class 20 or better planet that has over 50 base production in every category with a high number of asteroids nearby.

Other than that, you don't really gain much from levels to a single tile unless it is one of those leveled flats, so unless you've got an isolated +3 tile it's not advantageous to build a market in the middle of a research cluster.  You're gaining your 3% in return for losing 12% if you stick a market in the middle of 6 labs just to get a tile boost.  The only reasons to diverge are because you have two distinct groups of tiles where no adjacency boosts are lost, or two special resources giving higher boosts that will outweigh the lost adjacency.