Do not buy a higher-Ah battery just because you expect more torque. Amp-hours primarily describe battery capacity. For a homeowner, the most dependable reason to choose a larger compatible pack is longer runtime.
Why this question gets messy
Modern battery packs are not all built the same. Cell design, electronics and the tool itself can affect how much current a system can deliver. Some brands deliberately design certain tools and batteries to work together for higher performance.
That still does not make the blanket statement “more Ah equals more drill power” reliable.
What a larger battery definitely changes
Capacity and weight are the obvious changes. A bigger pack can run longer between charges, but it can also make a compact drill feel more bottom-heavy.
If the drill is too weak for the job, solve the job
If the drill repeatedly struggles with long structural screws or heavy fastening, the missing purchase may be an impact driver. If the problem is a dull hole saw, the missing purchase may be the bit. If the drill is simply old and worn, another battery may only postpone the replacement decision.
Use the drill-vs-impact-driver guide before treating the battery as a horsepower upgrade.
Think of Ah as the size of the fuel tank, not the engine size
That analogy is not electrically perfect, but it is useful for shopping. Amp-hours tell you about capacity. They do not, by themselves, tell you the torque of the drill. The tool, battery design and electronics work together.
When the larger pack is worth it
Choose a larger compatible pack when you are repeatedly stopping to recharge, when the job is far from an outlet, or when one battery needs to work across several tools for a long session.
When the smaller pack is nicer
For hanging pictures, assembling furniture or working overhead, a small battery can make a compact drill feel much better in the hand. Runtime you never use is just extra weight.
Sources used for this answer
Back to class: Cordless Drill Class.