Does storage capacity affect hard drive performance?

A generalisation isn't useful, but mostly when talking similar models/same series I'd say the larger drive would be faster due to higher data density in some way (be it more platters and heads, or just denser platters).

The bigger model would likely be newer as well and could benefit from firmware and other production improvements.

This is even more true in the world of SSD where the larger capacity options are generally faster due to more parallelism. On the other hand, sustained throughput isn't always the important factor of an SSD compared to mechanical drives but rather the low-latency on small random access read/write - which will be the same in most scenarios regardless of the number of chips.

Size is but one of numerous considerations in determining the actual realized performance of a drive.

Rotational speed is one of the factors that determines the write rate. A 15k RPM drive would likely be faster than a 10K RPM drive of the same specs and size. (Assuming all things are equal which they are not in most cases)

The next thing to consider is the expediency in which the voice coil can move the read/write heads for a seek or continued file access. The latency introduced by the moving voice coil read/write head is perhaps the most significant source of delays in the read/write process.

The electronic controller board and what connectivity BUS it supports is also another significant determination of speed. A good example is the various versions of SCSI disks which supported higher and higher speeds with every revision to the scsi standard. SAS drives offer aditional performance over SCSI,IDE and SATA because of increased BUS bandwidth.

The number of platters is indeed also a factor but not the most critical performance consideration.

You can not. Drive speed depends on lot of things, mostly on disk data density (is rotational speed is equal).

If you can, between two disks with same capacity, use one with lower number of platters.