If the barrel reins have knots, then I would definitely avoid those for roping. Sometimes you have to slip a few inches of rein when you're roping and I can only imagine how difficult that would be with knots in them, especially when you have the extra coils in that hand as well.
Not all barrel reins have knots in them.. my reins are were called barrel reins and they didn't have knots..
I think a lot of the time the leather ones are called roping reins and cotton/nylon/other materials are called barrel reins
If you get reins like this:
ALWAYS double check to make sure they are in the buckles securely (before EVERY ride) - these are famous around here for slipping and a rein coming undone - I've seen it probably half a dozen times in the middle of barrel & pole runs)
These come in the knotted and just one continuous flat rein - just be cautious of using them ;)
Personally, I don't like knotted reins - if I use them, then I "custom" knot them myself - I buy a pair of handmade ones in a 10-12ft length then add knots where I need them
Also I would not purchase flat nylon reins unless you plan on wearing gloves every ride - these can give horrible rope burns
IMO a nice set of cotton or leather reins is the best