Piece counts are the headline number in every tool listing, and they are close to meaningless on their own. A 132-piece kit and a 24-piece kit can do the same job, and occasionally the smaller one does it better.
What gets counted
A "piece" can be a screwdriver bit, an extension bar, a handle, a pry tool, a suction cup, a spudger, or — in the worst listings — the case. Two sets with the same number can have wildly different numbers of actual bits.
The useful question is not how many pieces, but how many bits, in which families, at which sizes. A set with 60 bits covering Phillips, flathead, Torx, hex and tri-wing is more use than a 120-piece set that is mostly duplicates of the four sizes you already own.
The three things worth checking instead
1. Bit families
Match the families to what you actually open. Electronics need Torx, tri-wing and pentalobe. Furniture and bikes need hex. General household is Phillips and flathead and little else.
2. Drive size
Most precision sets use 4 mm bits. Larger driver sets use 1/4". They are not interchangeable, and a bit from one will not fit a handle from the other. If you already own a driver, check before you buy a bit set for it.
3. Whether the handle ratchets
This matters more than twenty extra bits. A ratcheting handle lets you drive a screw in a confined space without lifting and repositioning the tool each turn.
Steel, briefly
CR-V (chrome vanadium) and S2 are the two you will see. S2 is harder and better suited to precision bits under torque; CR-V is tougher and standard on larger drivers and hex keys. Both are fine. Neither is a reason to pay twice as much.
Every set in Tools & Repair lists its bit families, drive size and whether the handle ratchets, alongside the piece count. The count is the count — if the name says 66 pieces, the description lists what those 66 pieces are.