Tl, DR: Sorcerers are specialists, not generalists, treat them as such and you will see the difference.

Disclaimer: If you dislike the Sorcerer because you think he’s just a weaker Wizard, this post is for you. If you dislike the Sorcerer because he needs planning to be efficient in stark contrast to his relationship with magic when it comes to flavor, or because he casts the same spells over and over and is therefore boring, I agree with you. I am also not saying that the Wizard is weak in any way. He’s great in many roles at the same time, but will (imo) never be the best at any single role.

Sorcerers have a low number of known spells, and a relatively small selection of spells to chose from. This is their weakness, and if you try to play them like wizards and take one spell from every school or role, you will feel weak. Sorcerers are specialists at the one role they choose, and in that role, they surpass Wizards almost always.

Metamagic is what makes Sorcerers special and makes them excel at the role they have chosen. While other classes can get access to Metamagic via Feats, the feat is incredibly limited, and takes up an important ASI slot. While a Wizard at level 1, 4 or 8 might take Metamagic Adept, a Sorcerer can increase their main casting stat that they use for literally everything or take other key Feats such as Warcaster. If your campaign starts at level 20, that’s no issue for the Wizard, but few campaigns do.

Metamagic is so strong because it breaks the rules of Magic in a game where Magic is already incredibly strong. Twinned spell gets around some concentration issues and saves spell slots. Subtle Spell violently breaks the rules of social encounters (this is no understatement). It also lets you assassinate most people in broad daylight. (Just take care to use a damaging spell that doesn’t visibly start in your space). It also lets you deal with Counterspell or having your Counterspell Counterspelled. Empowered spell takes Fireball, the best AOE dmg spell for much of the game and makes it ~20% stronger on its own. Quickened spell lets the Sorcerer be a lot safer and more flexible (Disengage/Dodge/hide action Cast spell bonus action) and vastly improves some spells (Sunbeam is twice as strong in the first round of casting). Careful spell lets you drop Hypnotic Pattern or Fear on clumps of creatures no matter where your allies stand. These are all powerful options to have, and things that Wizards don’t have access to without severely hurting themselves somewhere else.

To finish, a very short summary of Sorcerer specialist “roles” and why they are better (imo) than a Wizard at that specific role.

Blaster: Empowered Spell, Twinned Spell, Draconic Subclass. Deals more damage than Evocation Wizard. (Though Evocation Wizard does so safer via Sculpt Spells.) Easier Access to Elemental Adept to mitigate Resistances because you start with Constitution Proficiency and don’t rely as much on Resilient/Warcaster to help with Concentration Checks. Also, easier multiclassing with Warlock for Eldritch Blast spam.

Controller: Careful Spell, Heightened Spell. Can drop huge AOE disables anywhere he pleases without bothering allies, has at will access to giving an enemy disadvantage on save vs key spell. Wizards can’t do any of that (Portent could in theory, but it’s unreliable if you specifically want to make enemies fail saves and only that).

Social roles (Investigator, Instigator, Trickster, Party Face, Assassin): Subtle Spell. Wizard in theory has more tools to solve problems, but will struggle to apply them consistently, because casting in public likely has consequences. Sorcerers being a CHA class is also a benefit here because you can lie your way out of problems. Only caveat is that if you play a magical detective and you interact way more with places than with people and need the Investigation skill.

Buffer: Twinned Spell, Quickened Spell. Being able to cast Haste/Polymorph on two targets with one spell slot and then being able to keep concentration with your Con proficiency and ability to hide/dodge/disengage while still being able to cast is incredible and something the Wizard can’t do. Becomes way stronger with Divine Soul subclass for more access to spells but isn’t required. Sidenote, Twinned Dragon’s Breath is hilarious and kinda good at level 3, and then becomes immediately useless at level 5.

So, when you build your Sorcerer and want to feel as strong as the Wizard, strongly consider specializing in one of these niches, but be prepared for the fact you will likely do the exact same thing in 90% of battles.