I play with a Ringtail Lizard wrap (very "pimp"!)...my first natural wrap, it was a gamble; but I'm glad I did it. I won't go back, it's a perfect balance between soft texture and durability, smooth enough to slide but pliant enough for a nice grip and touch. I like it better than leather. I condition it with saddle soap about twice a year. It's held up very nicely. Be careful with conditioners, they can make the wrap darken a bit.
I don't think embossed leather is the same; it's nice, but the extra price for the real deal is well worth it.
I love linen wraps (classic), but lizard wrap is my new favorite. Had a cork wrap once, hated it...it's the only wrap I KNOW I won't like having tried it. Leather wraps are all over the place with me...some are great, some not so much; depends on the grade, installation, and print.
I'd love to try stingray or elephant...something tells me I'd like it.