First, whether or not sinew actually helps performance depends on how it is used, what sort of bow it is glued on and what measures you're using to judge performance. Sinew is heavier per unit strength than wood, so if you put a sinew backing on a longer bow you are probably hurting performance more than helping, by any measure except durability. What sinew is good for is drawing a shorter bow into reflex and keeping it there, although even with shorter bows I suspect you're hurting cast.
Rawhide does not pull a bow into reflex quite like sinew does, but it can a little if you apply it right. Flax and other vegetable fibers are strong, but don't pull a bow into reflex and can actually overpower the belly wood of some species (as can sinew, for that matter), so vegetable fibers can be risky.
If you want the characteristics of sinew (pulls bow into reflex as it dries, diminishes performance of a bow relative to one of that same side-view profile made without sinew), there really is no substitute. At least none that I've found.
To be honest though, I think sinew backing is highly over-rated. I haven't done it myself in a few years, and am not planning any sinew-backed bows for the foreseeable future. If you choose a good piece of wood, let the wood thoroughly season, and design a bow for its intended use and for the type of wood you're using, sinew backing isn't necessary. I routinely make short bows, even bows under 40 inches long, without backing them with anything and they turn out fine and are quite durable.