Exeggutor

Throughout the generations, Exeggutor has shown itself to be in the top echelon of non-legendary Pokemon, excelling in both Grass- and Psychic-type specialist attacking roles. Unfortunately, it's fallen from grace in recent years with a number of better Grass and Psychic types shrinking its role more and more as time goes on. However, it's still a good budget Pokemon.

On defense, Exeggutor isn’t as fearsome as it once was now that good Dark- and Bug-types lurk in wait. However, unprepared attackers will still be left stinging from a barrage of Confusion and Seed Bomb backed by a big Atk stat.

Best PvE Offensive Moveset

• Confusion should pair with Psychic for a Psychic Type attacking set.
• Bullet Seed should pair with Solar Beam for Grass Type damage.
• Seed Bomb comes out far more frequently than Solar Beam, meaning it will occasionally out-perform Solar Beam if Exeggutor drops while it has a lot of energy saved up.
• Extrasensory and Zen Headbutt* are objectively worse than Confusion.

Best PvE Defensive Moveset

• Confusion is simply the best defensive fast move in the game.
• Of the other fast moves, Extrasensory is a distant second.
• Seed Bomb is the most threatening defensive charge move, firing early and often on top of being hard to dodge.
• Psychic is a good move with relevant defensive coverage.
• Exeggutor may not survive long enough to use Solar Beam.

Confusion is an objectively great move in PVP thanks to its great damage output and good energy generation. Bullet Seed offers superior energy generation, but the lack of damage output is discouraging. 

It pairs well with Seed Bomb to pressure shields while dealing solid damage. Psychic hits hard coming off of STAB, and it can provide some shield-baiting opportunities.