Hey Rangr, welcome to the site!
You may get a number of different answers on that. That's because there's a number of ways to go about it. First, the flipline can be permanantly affixed to one side of your saddle and the other side removable and adjustable, or neither side is permanently connected (each side removable).
The classic dudes, the purists (in a rope sense) will use a section of regular climbing rope as the flipline and adjust with a smaller diameter rope prussik or friction hitch which attaches to the saddle via a caribiner or snap. The other end of the flipline is permanently connected to the saddle. The more mod purists will have a prussik-type rope adjuster on
each side of the saddle, and either side can be removed and either side can be adjusted. This is called a dual-ended, dual-adjustable flipline (DEDA). Then there's a dual-ended, one side adjustable. Then there's the most common, single ended, single adjustable. The dual adjustables are almost always rope-prussik adjusters on rope flipline, but you can also use rope-prussik adjusters on wirecore fliplines.
Besides the rope-prussik adjusters, there's
mechanical adjusters, usually a Petzl micrograb, or a Gibb's-type adjuster, basically a one-way, compact ascender that is adjustable one-handed. It is permanently on the flipline and connects to the saddle via a triple-lock caribiner, though I have seen some setups where the climber connects on and off with a quicklink (Maillon Rapide). The quicklink is anything but quick. Klimair has a dual-direction ascender device that you can use on a dual-ended flipline. With this setup, you can adjust with either hand, depending on which side the adjuster is on, with the versatility of being able to disconnect from either side of your saddle. This, I guess, would be a single adjuster, dual sided ajustability, dual ended flipline, with an acronym that would be rather ugly.
No one uses leather buckstraps anymore, except for a few remaing cavemen. Most, I imagine, use rope fliplines because of the economy, but many use wirecore, which is wire rope (steel cable) with rope braided around it, making it
look just like rope, but it's terminated around streel thimbles and industrially swaged. These 'flip' better and give the climber a higher sense of confidence as a chainsaw has a pretty tough time cutting through them. Rope fliplines, on the other hand, are not as forgiving if you make that mistake.
I have tried a number of these systems, so to have a personal ability to compare and contrast. That doesn't mean I can tell you what's better, because a lot of it boils down to personal preference, what the climber thinks he or she can afford, what they know of what's available.
Personally, I think wirecore fliplines are the way to go, even though I've been on rope fliplines for the past two years. Wirecores are more expensive, and the dual-ended wire-cores (yum) are really hard to find. They're heavier, too, as in addition to the metal core and metal thimbles, each end has a metal (usually steel) safety snap. The weight and cost, compared to the bombproof feeling of safety, and the confidence that brings, make it a worthwhile investment. Ya just gotta keep your saw away from your flipline, wirecore or rope (duh!).
Back to your adjuster question, Tree Machine likes the compact, aluminum
Petzl Micrograb, probably the most popular of all flipline adjusters, and for good reason. Affordable, lightweight, compact, one-handed, paired with an aluminum triple-lock and the very important, but often overlooked captive thingy, or trap (stainless steel, rubber, leather or plastic) to hold the biner
captive in the adjuster so it doesn't flip around. The most important facet of the system is your ability to put it on, off, and adjust it with one hand.
Here's a pic from a couple days ago, a whacky-big takedown, photo credit to Alex, brush schlepper extraordinaire and pretty good with the camera. I'd just attached the bull rope onto that limb and was removing the flipline so as to avoid an unnecessary flight.
