Mammoths are useless now when it comes to getting wood. Rather have my pre-TLC mammoth before that gather 90% wood and 10% thatch than getting a saddle with a drum, and a scream that is pretty useless.
You can use a stegosaurus to gather woods, using the heavy plates mode. They don't have weight reduction, however, they have a lot of weight. Moreover it gathers so much wood! It's amazing, I have a stego named Stella and every tree give me almost 100 woods and she can hold between 800 to 700 woods inside it's inventory.
Even though Casteroids are better at collecting wood, mammoths can carry so much more, and have higher weight reduction. They also move faster and have a larger attack range. When gathering wood on a mammoth, I personally have found that it’s stomp, or left trigger (Xbox) attack gathers more than its main attack
Therisinosaurus collect wood very fast and very effective, but with it it becomes encumbered very fast too. Mammoth collect it not very fast, but it has big radius of attack and it can takes large amounts of wood with its high weight and weight reduction of wood in its inventory.
Okay so Stego hardened plates is pretty good. I'm currently using my lvl.40 Stego and i get 46 or so wood with one swing on one tree he has 202.2 Melee idk if that effects anything but i haven't put a lvl in his Melee so Stego good but get the others like mammoth or something as soom as possible. Hardened Stego is good but has no weight reduction. Which kinda sucks. Also i just checked again with my lvl.40 stego he actually gathers 42-74 per tree & swipe.