Sorcerers get the ability to Twin Spell, a free Mage Armor, extra HP, or the ability to randomly TPK your entire level 1 party because the wild surge table is BS.
Wizards get familiars. Unlike in past editions where losing your familiar was such a terrible thing that they were relegated to pure RP tools, wizards in 5e are meant to use their familiars and not worry too much if they die.
Familiars require a great deal of DM discretion to handle appropriately. At their most basic, a familiar grants advantage on one attack roll, once per turn, against an enemy within 5 feet of the wizard. This isn't OP, this is the most simple, basic thing that any familiar can and should be doing. IMO a DM shouldn't normally go out of their way to kill a familiar just granting advantage once per turn, but you do you.
If the wizard had the good sense to pick an Owl familiar, they grant advantage once per turn, to one attack roll, against any one enemy, to any one ally, and they stay safe while doing it. The Owl is indisputably the most mechanically strong familiar. Don't be salty, just run with it.
As useful as the Owl is in many situations, this is where sensible DMing comes in. An owl flying through a dungeon should attract some attention regardless of it's stealth stats. A rat should be able to sneak through virtually any urban environment, and many dungeons, without even needing to roll. A raven should be able to relay messages with its mimicry. A spider or lizard should be an absolute Boss at scouting dungeons. The Hawk can carry more than any other familiar due to its strength. You can milk a poisonous snake for doses of venom between adventures. Every familiar has different strengths, no single form wins in all situations.
When it comes to Ability checks, it definitely gets dicey. Familiars tend to be small, and that really limits what they can do. On the other hand, creativity goes a long ways. Their small size means virtually any familiar should be able to assist with Perception or Investigation. Performance is almost a given if you're doing a stage-show. Pecking the eyes of someone grappling you could give advantage on an Athletics or Acrobatics check to escape. Their extra-planar nature might let them help with Arcana, Nature, or Religion checks(infernal, fey, or celestial nature). A cat, rat, or owl could probably assist with Stealth. Many of them could help with Survival. And so on.
Or you could simply rule away all of that and not let them assist with ability checks because it's a pain in the butt and/or too powerful. Frankly, the concept of Familiars as independent creatures really isn't handled or addressed very well by the 5e rules, and they did it intentionally. You're the DM, you decide what they can do.