Which stamp on gold means that the gold is better, 14K or 585?

They mean exactly the same thing, but are just different ways of measuring the pure gold content.

585 means that the metal is 58.5% pure gold, 14k means that 14 parts out of 24 are pure gold. 14k strictly works out as 58.3% but the difference is due to the convention that usually rounds the numeric system to the nearest half a percentage point. That makes it far easier to do quick mental arithmetic when calculating prices; both systems existed long before everyone had a pocket calculator within easy reach.

There are exceptions to the half point rounding: first is that pure 24k gold is never totally pure so is always described as 999 or for the purest samples, 9999, and less traditional newer alloys such as 10k (9k is the norm) and 22k (in the past the scale used to go straight from 18k to 24k) get listed as 416 or 417 for 10k and 916 or 917 for 22k.

In reality the difference between 14k and 585 is usually non-existent, and when trading large amounts buyers usually get an accurate assay anyway of the true content to calculate prices. But due to uneven mixing a 1kg bar of 14k gold may assay as less than 58.3% at one sample point and could be more than 58.5% at another sampling point., so for large quantities multiple samples are taken and then averaged.

Unless the purity mark is provably from a trusted reliable assay house such as the UK's Hallmarking scheme, you can never really trust the declared gold content anyway and even UK hallmarks are easily faked.

Both mean the same. 14K is the US mark and 585 is the European mark for the same quality.

585 is slightly better as 14K gold is 57.