Relic weapon: what should I do?

[Atoli]

Don't do either of them. Get one of the weapons that are much easier to obtain and use the time you would have spent grinding relic doing something that's actually fun.

Except that..you can totally do whatever you consider fun and that will progress the relic, because you can do the 60 relic steps with just about any content

Also, other weapons are random, stats may suck in one patch or be good in another. Relic is always an alternative stat set-up, and in later stages even let's you choose your own stats.
AND unless you do really well in raiding (which most of the playerbase does not), Relic is the only way to obtain a weapon with a similar item level in the same patch.
So yes, it is actually worth it (the 60 one, not the 50 one).

And even if you did, all it would do is reduce the amount of FATEs you need to do at 60 for the first step of the Anima weapon.

No it actually let's you skip that step completely. Not a single fate needs to be done
But since the step was nerfed, you get a crystal in nearly every FATE, so it will only take 1-2 hours to finish the first step now.