Bearing in mind that I'm no expert, this is my experience with friction knots...
It depends on the friction hitch. I've only used a Blakes and a Distel for any length of time but the principles are the same for most knots.
I currently use a Blakes with roughly the same diameter as my lifeline... with a smaller split tail, a blakes seizes up easily and you'll be constantly loosening it. Same probably goes for a tautline.
A Distel works with same or smaller diameter. I use a distel on my lanyard adjusters at the same dia as my lanyard rope. I used to use an 8mm beeline distel for my split tail on Poison Ivy but it got to where it locked up on me more than I liked... I weigh 185.
The smaller the split tail diameter, the better gripping power, for lack of a better term. If you go to a smaller diameter you have to compensate with more turns (more surface area) in the knot to keep the friction the same or the knot will have to be tighter and more likely to lock up. The less surface area between the split tail and the lifeline, the tighter the knot will have to get to make enough friction to hold your weight. A small split tail diameter will support a lighter climber and still loosen easily but for a bigger climber it will tighten and seize more easily.
Best thing to do is experiment. I tried several different hitch cords with a Distel and a Blakes and for me, 1/2" Tenex (actually 3/8" buried full length inside itself) tied with a Blakes Hitch on 12mm Velocity or Poison Ivy is the ticket. When I double crotch I use my rope on a bridge instead of carrying a second split tail. Either way, the Blakes will generally only tighten up and lock if I have a jerky stop but the Tenex loosens easily with one hand.
I keep thinking I'll try a VT because I hear so much good about it but really, what I have now works as well as I want it to... besides, splicing Tenex is a snap.