You could just write your own method for Base64 as well… but I’d generally recommend using external, well-tested libraries for both. (It’s not like there’s any shortage of them.)
The difference between Base64 and hex is really just how bytes are represented. Hex is another way of saying “Base16”. Hex will take two characters for each byte – Base64 takes 4 characters for every 3 bytes, so it’s more efficient than hex. Assuming you’re using UTF-8 to encode the XML document, a 100K file will take 200K to encode in hex, or 133K in Base64. Of course it may well be that you don’t care about the space efficiency – in many cases it won’t matter. If it does matter, then clearly Base64 is better on that front. (There are alternatives which are even more efficient, but they’re not as common.)