One of the biggest necessities we've found over the years, is that with horses the fence needs to be high enough to discourage leaning over or pushing. 5' works for most of the taller horses.
I think our non-climb horse wire may be the same as the 'red' fence you refer to. It's a 2 x 4 mesh also, but is NOT a 'welded' wire mesh. Ours, ounted on wooden posts, has been up about 12 years, but I really think it's longevity is definitely linked to having the top reinforeced, even though the top is 5' high, and having the bottom up off the ground. We do have a few stretched, bowed spots from horses scratching their rear ends on it.
V-mesh is also long lasting, but much more expensinve than the non-climb horse fence. We've also known of young horses to get their teeth caught in the v-mesh (we're in an area near lots of racing QH breeders who use it).
Whether or not a horse runs into a fence has a lot of factors .... visibility being EXTREMELY important .... size of the paddock/pasture being another...location of the paddock .... whether the horse is out 24/7 or turned out sporadically ... all have a bearing on the horse's actions/abilities to avoid a fence 'crash'.....also knowing each individual's response to various situations.
During Chrissi's years as a working student for a former Olympian's Eventing barn as well as her time as assistent trainer at a Grand Prix Jumper barn, she quickly learned that stalled show horses, even those being regularly worked and exercised, are the most likely to have a 'fence crash' when turned out ... they simply get too excited with their 'freedom', and the younger the horse, the more likely the accident. At both barns, they had grooms or working students who supervised the ENTIRE turn out time for the show strings, just incase of an accident. One of these barns had all classic wood fences, the other pipe and cable. Both facilities were impecably maintained, but it was still positively necessary to constantly supervise the show horses during their turnout. Natually, both the above facilities RARELY had an accident, and those very minor, but only because of their close supervision of the show horses.
The Eventing farm also had a small group of broodmares and young stock who were out in good sized pastures 24/7 in summer and most the time in winter. These mares and youngsters did not have any 'fence' collisions, regardless of the fencing materials. 'Course they also weren't bothered by outside influences like helicopters, chasing dogs, motorcycles, etc. which would add another dimension.
In all cases, we've found that horses that have been exposed to a variety of stimuli while growing up (kids, dogs, lawn and building equipment, motorcycles, strange animals and fowl, flapping tarps, even gunfire/fireworks in the company of CALM humans/hoses) are much less prone to 'accidents' or ulcers period. After 40 years, we've had only ONE fairly serious fence collision and that was over 30 years ago involving three weanlings racing around a fairly small paddock. One slipped in a corner only because she was crowded by the others and could not maneuver freely.