Which one of those is preferable? It seems to me that they are both historically based. 10 x 10 is also 100 in base-12 (it's only in base-10 that it looks like 144).

IMHO, in a modern setting base-16 would be the most convenient. Then I maybe wouldn't struggle to remember that the CIDR range C0.A8.0.0/18 (192.168.0.0/24) consists of 10 (16) blocks of size 10 (16).

There’s nothing particularly convenient about base-ten; for real-world uses base-twelve would be preferable thanks to its large number of divisors (and even larger number of divisors of its multiples like 60). Which is exactly why 12 and 60 historically appear in many contexts.

A number theorist would probably want a prime base, so that N (mod 10) would be a field.

A power-of-two base wouldn’t be particularly convenient to anyone except a small minority consisting mostly of hardware and software engineers.

There is one particularly convenient fact of having ten digits.

Fair :P I should've said "inherently convenient".

> base-16 would be the most convenient

That would mean 1/5=0.(3)₁₆ would be an infinite fraction as well. A more convenient would be 6 or 12 because it allows to represent 1/3 exactly.