Rogue and Fighter are the best. They get extra lower-level ASIs. They also have the Arcane Trickster and Eldritch Knight subclasses, which are above-and beyond the best subclasses in the game.
Fighter has the best Level 1-2 class features, before they even get subclass features. The only class feature that is as good as any of the Level 1-2 Fighter class features is the Divine Smite class feature of Paladins, but Action Surge is its equal. Rogue has good Level 1-2 class features -- but not-quite as good as Fighter. Rogue's 3d6 Sneak Attack damage combined with Uncanny Dodge at Level 5 is great, but I don't think much beats the Evasion class feature at Level 7. I, personally, would rather have Evasion than any 3rd or 4th level spell combination.
After Levels 8 and 10, the Fighter and Rogue start to fade in efficiency, especially without more-oomph like the Eldritch Knight and Arcane Trickster subclasses. Just as a small example, the Monk Way of the Long Death gets the Mastery of Death subclass feature at Level 11. Fighter and Rogue can't really touch that level of class-craft mastery.
The Sorcerer is my favorite higher-level class, especially with a heavy focus on teleportation spells. There are a lot of multiclass combinations that are exciting and fun. Almost anything with Arcana Cleric feels broken at times. Going Gloom Stalker to 4 and then Arcane Archer for the rest can be exciting. Probably the best is Cleric with Tempest Domain multiclassed to Wizard with the School of Evocation subclass. It has a natural D&D feel without going too off-the rails -- and it's both fun and ultra-powerful. Sometimes I feel that the Charisma-prioritized (SAD) classes should never be multiclassed together. Not sure why Bard/Paladin/Sorcerer/Warlock is ever ok. Thanks, 5E, but no thanks.
Let's face it, though -- defense-wise Monk comes off well (with Fighter and Rogue not too-far behind depending on the challenges) and offense-wise it's a tossup between Barbarian, Fighter, and Paladin. For mystery and excitement, one can always play a Wild-Magic Sorcerer. Yes, a well-placed Sleep or Color Spray early-on (and sometimes even mid-level) can be devastating, but the Wild-Magic Surge table is definitely the most-fantastic high-fantasy element in the 5E system. Don't prioritize Wild Magic every campaign, but I think a party needs this sort of randomness for 2 or more out of the 10 or so main 5E modules.
I don't like the dice-control elements in 5E. It's one thing to choose School of Divination Wizard subclass, but it's another to layer Lucky / etc on-top of that. Too-much. Advantage and disadvantage are good, which is why Enhance Ability is one of the best spells in the game and why I keep giving Mastermind a second and third look -- but Elven Accuracy and similar make me cringe a little here-and there. Again, it's too-much for me and what I like in gaming.