TPE
Thermoplastic elastomer (TPE) first became commercially available in the early 1950s, giving it a slightly longer history than TPU. TPE is generally lighter, softer, more flexible, and a bit easier to recycle than TPU. However, these desirable qualities come with some sacrifices: Compared to TPU, TPE is less resistant to abrasion, grease, oils, chemicals, and extreme temperatures, especially cold.
TPU
Thermoplastic polyurethane (TPU) was introduced in 1959, a bit later than TPE, but it has gained immense popularity since then, serving as a bridge between flexible rubber thermoplastics and rigid plastics. TPU offers superior resistance to high and low temperatures, ozone, grease, oils, chemicals, and abrasion, making it a great replacement for hard rubber. TPU also has greater load-bearing capacity than most comparable materials. However, TPU is less flexible than TPE, and while its rigidity is highly desirable in many applications, it's less soft to the touch.