I, too, can give some opinions. I have not used all types of harness but have had exposure to many in training and while attending events. I've asked questions of folks at many events - plow days w/ pleasure and work harness; CDE's; carriage driving classes at breed shows; even asking questions of many AMHR/ASPC & Hackney owners as long ago as the 80's & 90's.
I got a Hackney pony mare in 97 that came with a leather, nylon & cord training harness and jog cart and a leather show harness and Jerald show cart. Both were minus the breeching and worked with wrap straps to pull the cart more from the gig saddle then from the breast collar. When in a wreck with a young mare on her 3rd hitching (hit a ground wasp nest and it was UGLY) - none of the leather broke and I lost my pocket knife during the wild, runaway ride. We ended up in a heap with her legs in many places they shouldn't have been though no breaks of anything. Parts I wish had stretched had not and getting her loose, especially w/ how much I was shaking and the reaction I was having to wasp stings, was difficult. Time stood still - have no idea how long it took. May have been hours; may have been minutes (prob in-between - our young daughters DID go 2 miles up the road to get help - I was mostly done with getting her freed by the time it arrived). Eventually got the cart and her upright and then fully unhooked. She had scrapes (probably some bruises), lots of wasp stings but no major injuries. She had more damage to her young mind - I was not able to get her driving again - both of us were scared "spitless", but she did go on to become a wonderful little hunter/jumper and from what I understand is still packing young riders. I was able to go back to driving both her sire and her dam, but easily gave it up for years when kids wanted to go on riding and couldn't afford to do both... Sold the show equipment and "buried" the training gear... Loaned out my training cart for a couple of years as well...
Years later in 2009, I was so broke when I started driving, that I took used hay string (from large round bales), washed it, braided it and used that for starting our driving ponies. Once I had gotten over my own fear - both with lessons w/ other horses and ponies - and with starting our own (I had continued using ground driving for starting riding ponies), and we knew that I'd continue with driving, I started investing in harness. I also went to Draft horse driving events in our local areas and CDE's in Southern Pines, other driving events around NC. During all of this I used various types of nylon, bio/beta and leather and chain/rope.
In all harness, there are quality levels for all types and in all materials from leather to bio. I have found some will break and some will stretch BUT in all cases of the types I've used and looked at there have been incidents where it has broken when least expected or wanted and other times when it hasn't broken and could not be cut easily w/ any type of knife.
I chose to go with bio AND beta harness (they are different). I have issues with time and tack storage that make leather a PITA to take care of. I love the bio and beta for easy cleaning. Just as in leather, bio/beta has break and stretch points. The higher the quality of material - even single layers - the less likely to break or stretch. The more layers - the tougher it is to break, stretch OR cut. Lower end bio/beta, just as in leather and nylon, have large clunky bridles that are difficult to fit. The higher end products are every bit as nice as the leather can be. Leather & nylon bridles can also be large and clunky. Some of the new beta lines are just as "alive" as a good set of leather ones - I don't have any of those. Some are just as "slick" as leather when driving (or riding) in the rain!
Just as in riding, I move my lines constantly while adjusting to what I'm asking our ponies to do. I move my hands, but use the slide and take up methods much more. I hate hand loops attached - may work OK in the breed ring (haven't shown that way - doubt that I'd use hand loops, though). I think driving lines with strips sewn thru the ends like on an english or dressage bridle rein, would work wonderfully in the rain. But have neither seen nor tried that myself - just think it. The rubber grips of the bio/beta are really nice on cross country riding reins, bet they would be on driving lines as well - again I don't know since I haven't tried them myself.
And those FIRST two haystring braided harness (made in 2009 & 2010) are still in use for starting the youngsters. They take a beating and continue to work well. I've had to redo both driving lines (left them hanging on the round pen & young ponies chewed parts of them up) and the one set of single layer traces which wore out on both ends with some of the wild rodeos we had when first hooking to objects. I've replaced both the felt/nylon training surcingles I had and need to replace them again this year (3rd time).