I buy a lot of steel bar, usually in full lengths unless we are talking 4" plus. Most unless specially ordered is what is know in the trade as GCQ which stands for General Commercial Quality is is generally EN3B.
Black steel or hot rolled is also EN3 or EN3B, never been sure of the difference. I never use EN1 leaded as a lot of my work is shafts and because the lead gives it very good machining qualities it also makes it very soft so pressing a shaft in for an interference fit will invariable bell the shaft or bend it.
The next statement is something I have found over time and have no proof as to whether my interpretation of it is right or not just that it works for me.
Many people say black steel doesn't machine well and is gummy which I fully agree with up to a point. And that point is size.
I have some black steel here 16mm round, bought in for some window bar jobs. It saws well, welds well which is ideal for the job but turns like crap. HSS, tipped, new tip, doesn't matter, looks like wrought iron.
Now the next size I carry which is 25mm, [ pity I don't have any 20mm as a test ] turns fine and when you get up to 50mm if you belt the speeds and feeds right up you can get a mirror finish on it far better than bright drawn and more like EN8.
Now the unproven statement.
I put it down to how fast the bar cools when it comes off the rollers. The thicker the bar, the slower and the better finish. That's why I say I'd like to test some 19mm or 20mm to find this cut off point.
For me and my supplier who I presume buys off the same major stock holders as everyone else 16mm is rubbish at turning but 25 is OK, 30 is even far better.
I can save a serious amount of cash using black. Bright comes in nominal 3 metre lengths and black is roughly the same price but comes in nominal 7 metre lengths.