Incidentally, don't our Pokemon profiles include abilities granted by IQ Groups?
https://bulbapedia.bulbagarden.net/wiki/IQ#IQ_groups
Smeargle is IQ Group F, Ditto is IQ Group A.
To be comprehensive, let's go over some relevant skills for both sides(The stars are just from the "When Learned" section.):
Ditto
1. Dedicated Traveler Base Skill
Prioritizes moving over using attacks or items.
2. Acute Sniffer 50 (☆0.5)
Lets you know the number of items on the floor. (I'd presume this means it knows what useable items are available to it in the location. Although, what stuff could it find that's useable?)
3. Survivalist 140 (☆1.5)
Restores more Belly stat when eating food. Sometimes avoids getting status changes when eating Grimy Food. (May be useful if it turns into a battle of attrition.)
4. Map Surveyor 580 (☆6)
Knows the floor layout. (I'd presume this means Ditto knows the layout of Central Park by being there.)
Smeargle
1. Wary Fighter 180 (☆2)
User steps back one tile when it misses a move. (So if Ditto dodges, Smeargle might step back?)
2. Sharpshooter 260 (☆3)
Raises critical-hit ratio.
3. Hit-and-Runner 270 (☆3)
Sometimes cancels foe's counter-attacks.
Both
1. Item Catcher Base Skill
Can catch a Throwing Item and keep it for its own.
2. Item Master Base Skill
Can use and throw its held item. (Ditto may be carrying Metal or Swift Powder. Smeargle doesn't carry any items, so this may give it a range advantage.)
3. Exclusive Move-User Base Skill
Uses only moves, not regular attacks. (Note: This is listed as affecting Partner Pokemon, which are normally AI; Presumably, Pokemon of the same species with the same skills that are player controlled can also use Regular Attacks, so I'd reason a normal Pokemon could ignore this limitation if it wanted.)
4. PP Saver 55 (☆0.5)
Sometimes gets to use a move without draining PP.
5. Multitalent 310 (☆3.5)
Adds 5 to Pokémon's max PP. Cannot be turned off.
6. All-Terrain Hiker 400 (☆4)
Can cross water, lava and valleys. (SBA puts default location as Central Park. So Ditto being able to walk on water, especially if it can throw things is helpful.)
7. Pierce Hurler 850 (☆8.5)
Throwing items penetrate Pokémon and walls and continues flying.
So Ditto prioritizes moves over attacks or items (But this might be AI induced stupidity, as it's an AI partner only skill; Players can ignore it, so why wouldn't regular, reasonable Pokemon?), knows the layout, where all the items are, & is better at eating food.
Smeargle will react to Ditto dodging better, crit more often, & can sometimes cancel "counter-attacks", if Ditto has anything that counts as those.
And both of them can catch & throw items, as well as throw them such that the thrown item penetrates Pokemon & Walls; This might stop catching. May be useful for Ditto, as it's the only one with a Held Item, & thus, may have a range advantage.
Both of them also have a chance to use a move without losing PP, & both have 5 extra PP.
They can also both cross water.
So in theory, a large portion of this match could just be Smeargle and Ditto standing on the water of Central Park Lake, trying to kill each other by tossing the same pile of powder back & forth at one another.
The best way for Ditto to use its abilities would be to stay away from Smeargle, & exploit its knowledge of the layout & where all the items are so it can use them or chuck them at Smeargle. I'm not sure if that uses PP, but neither do Mystery Dungeon basic attacks, so both can last quite a while.