I will say, I prefer Arko to Williams, but the Williams I have tried is the modern stuff. I will keep my eyes open for some Vintage Williams.
I am with these classy folks right here. Williams old or new wins hands down all the time every time. To the folks that have never tried what are you waiting on. Williams has been around since the 1840's for a reason. It was the first to make a cake for use as shave soap and is THE classic.
I voted Arko, but like them both for different reasons. With modern Williams, I can get a pretty darned great lather even though our water is extremely hard. I tried lathering it with bottled water and it didnt seem to make any difference. I dont exactly get the fluffy, "yogurty" lather but its still a really nice shave lather and doesnt dissipate etc. I like Williams because I could get it at my local supermarket for $1.09/puck. They dont carry it anymore, but I have about 15. I think the nod goes to Arko for me, though. I love the scent, I enjoy using it to face lather, and of course love the lather properties. Arko leaves my face clean with no residue etc. We all know how great its prices are. I have about 10 sticks, but havent purchased a tub. For soaps in this price range, Ill keep my vote for Arko, but still enjoy using them both fairly regularly with all the rest in my den.
I used what we call now Vintage Williams (2 for 25 cents when I started out) for many years and had no problem with getting a great lather but when I noticed the change to the new Williams I started looking for other soaps. I landed on Arko Stick and after bowl pressing it I get a great lather much faster than I can with new Williams. Other than Arko I also use Cella(kilo) Vito's (kilo) , VDH and sometimes I'll give new Williams a go.
Arko has some nasty stuff in it. I've used Williams, but there is so much better stuff out there. It is like asking if I enjoy McDonalds or BurgerKing when there is a nice Greek or Italian restaurant next door ..... heck even the Mom and Pop's diner is so much better. This isn't 50 to 75 years ago when you went to town and only had two or three choices; you literally have well over a hundred brands to choose from each with a dozen different scents delivered to your door.