Help Me to Decide Which Archer Crits the BEST

Both have their pros and cons I would say, overall Billy has the greater one turn Crit damage burst (maybe best in the game) I think due to 2 of his skills increasing Crit damage by a total of around 150% but only for a turn, and thus requires some set up beforehand. His np is also single target which may be preferable to you in boss fights. However, as I said after that initial burst he doesn't have much in the tank and his c.star generation is quite poor.

Whereas Emiya and I'm presuming you've done all his Strengthening and Interludes has a better all-around skillset I would say his Hawkeye B+ increases his own critical star generation rate for 3 turns and also increases own critical damage for 3 turns thus having more sustainable crit damage and c.star generation. He has better survivability too. His NP is aoe and so take from that what you will obviously not the best for single target damage.

Both have reasonable Np gain aswell Emiyas 3 Arts cards and Billys Quickdraw Skill.

Ultimately it's up to you and your preference, I would go with Emiya but perhaps thats who I like better and is not the most efficient option. Hope any of this helps you make up your mind and maybe someone else can improve upon what I have thought, Good luck.

Between the two that you mentioned, I'd go with Emiya. It's true that Billy's crit damage steroid is a bit higher than Emiya's, but you also have to remember that Emiya's base attack is 22% higher than Billy's (when they're both level 100), so I suspect that Emiya probably still crits harder. Plus Emiya's deck is a bit better, imo, because Billy's double quick cards are kind of lame. And the fact that Emiya's crit steroid lasts for 3 turns is an obvious advantage. And last but not least, Billy looks like a goober, and Emiya looks like a badass.