Few Pokémon have as a storied history as Zapdos. Overused every generation except 5, shows up on many VGC teams throughout the generations and has just been all around excellent. The Generational shift has been a mostly positive affair for Zapdos. A regional variant is always something worth celebrating, and access to Weather Ball and Special Flying STAB in Hurricane are downright fantastic. On the other hand, the loss of Hidden Power hurts a bit as Zapdos loses its Ice coverage and best option for taking out threats like Garchomp, Dragonite, and opposing Zapdos.
The Warding Storm
Zapdos
Ability: Pressure/ Static
Item: Heavy Duty Boots
-Roost
-Thunderbolt/Discharge
-Heat Wave/Hurricane
-Defog/Toxic (transfer only)
EVs: 252 HP/216 DEF/40 SPE
Nature: Timid (+SPE, -ATK)
Zapdos makes a fantastic defensive pivot, resisting Bug, Grass, Fighting, Flying, Steel and Ground type attacks. So what does this resist? Rillaboom, Kartana, Corviknight, Buzzwole (Ice Punch only does 34.3 - 40.6%), Hawlucha, G-Zapdos, Jirachi, and Scizor. Being able to check so many Physical threats gives Zapdos a niche that is hard to replicate (all of the other Flying Electric types are too frail to pull this stunt off).
Roost is the most important part of the set, enabling Zapdos to take repeated hits and heal back up. Thunderbolt and Discharge are your Electric STAB of choice. Thunderbolt is more powerful, but Discharge is good for spreading Paralysis. Heat Wave and Hurricane are the coverage moves up for consideration. Hurricane is far stronger, but more inaccurate outside of rain, while Heat Wave hits Steel type targets much harder. Defog gives Zapdos valuable team utility by removing Entry Hazards, Screens and Terrain, while Toxic ruins many a defensive check that would like to switch in (like Hippowdon, Blissey and Swampert) (most Steel types don't like switching into Zapdos due to Heat Wave). Both moves are transfer only, so do keep that in mind.
Heavy Duty boots enables Zapdos to ignore Stealth Rock and makes Defog duty easier. A positive speed nature and 40 EVs enables Zapdos to outspeed Adamant Banded Rillaboom, whose Wood Hammers can 2HKO in Grassy terrain. This enables Zapdos to be a more consistent check vs Rillaboom. Otherwise, EVs are to maximize bulk.
Other Options
Volt Switch -If you don't have access to transfer Zapdos, then Volt Switch is a good 4th move, enabling Zapdos to predict counter switches and pivot out while maintaining momentum.
Splitting Bolt
Zapdos
Ability: Static/Pressure
Item: Life Orb
-Hurricane
-Heat Wave
-Discharge/Thunder/Thunderbolt
-Detect
EVs: 4 HP/252 SATK/252 SPE
Nature: Timid (+SPE, -ATK) or Modest (+SATK, -ATK)
Zapdos makes a fantastic pokémon in doubles. This set is meant to Dynamax right off the bat and start spamming Max Airstream Hurricanes, enabling Zapdos to perform Speed Control and provide offensive pressure in one moveslot. Heat Wave is a reliable Spread move that provides valuable coverage vs the many Steel types of the format. Your electric STAB is wholly reliant on your team makeup. Are you running ground types/pokémon with Lightning Rod/Motor Drive/Telepathy? Use Discharge. Are you running a rain team? Use Thunder. Neither of the above? Use Thunderbolt. Detect is as always valuable in VGC as Protect, even moreso as it cannot be locked out by Imprison except in the most niche circumstances.
EVs and Nature are the standard sweeper array to maximize speed and damage.
Other Options
Tailwind (transfer only) -If you prefer having something else Dyanamax, Zapdos proves to be a capable Tailwind setter on top of providing potent offense.
Weather Ball -if running a weather team, Zapdos is a natural fit on Rain teams with its access to Hurricane and Electric moves/Heat Wave to ward off opposing Water types/Ferrothorn.
Galarian Zapdos is quite the different beast from its Kantonian counterpart. Trading in an Electric STAB and sky high Special Attack for a new Fighting type and sky high physical Attack, Galarian Zapdos has its own checks and counters. Defiant is an amazing ability on G-Zapdos, whose Kanto counter part has lacked setup moves to buff its offenses. However, its fighting type does come with a few downsides, a new weakness to Fairy is never desirable and losing the resistances to Flying and Steel is sorrowful. The new Dark resistance is quite welcomed considering how spammable Knock Off is this generation.
Co-op Kickboxing
Galarian Zapdos
Item: Choice Scarf/Life Orb
-Brave Bird
-Close Combat/Thunderous Kick
-Throat Chop/U-Turn/Stomping Tantrum
-Detect
EVs: 4 HP/252 ATK/252 SPE
Nature: Jolly (+SPE, -SATK) or Adamant (+ATK, -SATK)
Galarian Zapdos provides a similar role compression to normal Zapdos, able to provide Speed control and massive damage in one move with a Brave Bird powered Max Airstream. And unlike most other physical sweepers, G-Zapdos punishes Intimidate by actually gaining Attack, enabling it to maintain offensive presence. Fighting STAB is also amazing while Dynamaxing, as G-Zapdos essentially has STAB partywide Dragon Dance while Dynamaxed. Close Combat is preferred for power, but Thunderous Kick's defense drop means that G-Zapdos and its partners can break through sturdier targets. Coverage move is up to preference. Throat Chop provides coverage vs Psychic and Ghost targets that otherwise resist G-Zapdos' fighting STAB. U-Turn provides G-Zapdos with a quick pivot and chip damage in case of an unfavorable match up. Stomping Tantrum provides valuable Ground coverage and gets stronger if G-Zapdos rams into a Protect. Detect is on for the same reasons as Kantonian Zapdos.
Other Options
Low Sweep - If you would rather have something else Dynamax, G-Zapdos can still provide Speed control with STAB Low Sweep