For Doubles, Special Koko is better.
However, for Singles, either is fine and you'll have to look at the rest of your team and your opponent's team (as and when possible, or at least some knowledge of the types of teams being used in that format).
The reason Special Koko is better in doubles is due to its access to Discharge, Dazzling Gleam, and Electroweb, all of which hit multiple foes making it a stellar Pokemon as a partner.
For support it can run: Light Screen, Reflect, Electroweb, Nature's Madness, Safeguard, Rain Dance.
For offense, it can run: Discharge, Dazzling Gleam, Mirror Move, Nature Power (becoming Thunderbolt in terrain) and so on.
Back to singles, a case can be made for its effectiveness in both sets. Koko's attack is higher (115) than its Special Attack (95) by 20 points, which isn't that big a difference, comparatively. Due to Terrain boosts, Life Orb, and Choiced items, the power differential is negligible, and Nature and EVs play a bigger role in the stat total than the base stats themselves.
As an all out physical attacker, Wild Charge and Brave Bird are strong moves, with Iron Head for some coverage, Quick Attack for priority, and U-turn for pivoting. This set works best with a Life Orb, and it does have access to Roost as a form of reliable recovery in front of opposing defensive Pokemon, so the recoil damage can be recovered if need be. One thing to note here is that despite Brave Bird looking strong on paper, it's usually better to use STAB Terrain boosted Wild Charge as Flying only hits Fighting, Bug, and Grass type Pokemon super effectively, and Koko's only real competition in these types are Tapu Bulu and Mega Venusaur. In almost all other cases, Wild Charge + U-turn is more widely used.
In a metagame dominated by Landorus-T, Ice coverage became super important, but unfortunately Koko has no physical Ice moves, and its one Special Ice move is Hidden Power [Ice], which in the latest iteration of the game (Sw/Sh) is no longer viable.
That aside, Tapu Koko can still decimate opposition with Life Orb/Specs/ Zap Plate boosted Thunderbolt, Discharge, Dazzling Gleam, Grass Knot, and Volt Switch.
Finally, Koko can also serve as an excellent Dual Screen Pivot with Light Clay extended Reflect, Light Screen, Nature's Madness, and U-turn/Volt Switch.
If I was to make an assessment for either Physical or Special Koko, I'd personally go Special Koko. This is because even though in terms of raw damage output while Physical Koko might have a slight edge, competitive battling is a team effort of 3, 4 or 6 Pokemon, and Tapu Koko's greatest partners that form meta threatening offensive cores are Mega Medicham, Hawlucha, and Kyurem-B, all of which are incredible physical wall breakers, so a Special Koko with Screens and Volt Switch would complement these Pokemon exceedingly well, specially as they all deal with the aforementioned threats Koko has in the form of Bulu or Venusaur.
Of course, Special Koko also fares better against Landorus-T compared to Physical Koko, due to intimidate and the commonly carried Rocky Helmet (although neither can beat Scarf Lando).
Disclaimer: As I wasn't sure of which format was being mentioned, part of the analysis is based on Gen 7 OU, which was when Koko was in the height of its competitive prowess.