As a person whose climbed on most of the professional grade arborist ropes available for sale right now, and many others marketed for different purposes, I'd like to add a few things with several different perspectives in mind: arboriculture, recreactional climbing, and a few things I've learned about rope from my rock climbing buddies, more than one of whom are instructors at our local rock climbing gyms.
Static rope having almost no stretch is going to be the best in a system in which the rope is not traveling/moving, like in a srt system. Like someone else already said, you take a fall on a static rope, it hurts, but the thing to remember is that a static rope is not for fall arrest. It is technically intended for access only -- not ideal/optimum as work positioning w/ fall arrest. THe same is true of our tree saddles -- they are not approved as fall arrest harnesses, but rather work positioning harnesses.
Dynamic ropes for rock climbing are so stretchy that most tree climbers would be disgusted climbing on them in the first few minutes -- I've experimented with them. But those ropes are designed with the primary intention of providing fall arrest capability because the climber is climbing the wall -- not the rope. As tree climbers we are primarily doing a rope climb. Dynamic rock climbing rope is very very stretchy, very little shock to the climber on a fall.
Going off my personal experience, keeping in mind that my geared up weight is 190-220 and I'd rather climb on 11mm and smaller rope:
* Snakebite (a static rope) is going to give you the least stretch, but it doesnt tie knots well AT ALL. I've used it best for footlocking and srt with gri gris, ascenders, etc.
* Poison Ivy is about the lowest stretch arborist rope appropriate for DRT that I've found, its a good transition for guys that are used to climbing on 1/2 ropes. I've found that it gets fuzzy with hard use a little faster than Blaze, Velocity, and Lava. Its not terrible to footlock on either
* Blaze has about the longing lasting sheath, and its the cheapest. It will milk towards the end of 1-2 seasons if you are a much bigger guy than I am. But its durable, fast, and lightweight, and not very stretchy.
* Velocity is a little stretchy but not terrible, it has a higher wax content so its not very fast on a descent, its a great rope for winter climbing when theres snow and ice, and also for new guys to build confidence on bc its less likely to slip on a novice knot
* Lava is just a little too stretchy for ascents to me, I love the rope for work positioning, but not really for access. Its my long rope that I change to drt after I've footlocked or srt to the top of a big tree. Its durable, fast, and lightweight.
* fly is fairly stretchy and milks very fast imo.
*hy-vee is about the most stretchy arborist rope I've climbed on, True blue coming in second
* true blue is my least favorite climbing line because it is HEAVY, bulky, SLOW, and stretchy. Hy vee is a little lighter to me, but bulky, slow and very stretchy like true blue. I've put my true blue into service as a dirty rigging line, in conditions when I know there's going to be mud and/or sap lol.
* blue streak is not very stretchy, but kinda heavy and slow (to me)
* XTC spark is somewhat stretchy, but fire and spearmint definitely are. Kinda heavy and a little slow.
All that having been said, I use a different setup all the time. I've got a 90' Bluewater 10.4mm I use on the small stuff, very little stretch, drt or srt. On dirtier stuff like pines, I have a Blaze that I've had for awhile. For taller, bigger trees, I'll set the Sterling HTP and footlock or srt, or switch to drt on my Lava. Heres a pic of a setup I sometimes use for taller ascents.