In Tinkers' Construct, the top tier alloy, Manyullyn, has a mining level of 5, and a speed of 9. However, Cobalt is slightly faster, at the cost of a mining level. Is there any reason, aside from a durability increase, to use a Manyullyn pickaxe over a Cobalt one?
Manyullyn pickaxes have a vastly superior durability factor. With Tinker's Construct, Manyullyn is very nice for weaponry, but in this case, it's one of the best pickaxe head modifiers in the game.
It gives you the best mining level, fastest mining speed, and highest durability. You should combine it with a Slime handle and an obsidian binding, and then modify it with redstone, a mossball, a gold block, and diamond. This will provide one of the best pickaxes available.
TL;DR: Manyullyn is good for pickaxes because while it mines slightly slower than cobalt, it has a far higher durability, and can be modified to mine just as fast as cobalt.
In response to: "aside from a durability increase" from the OP:
Durability is extremely important and is basically the only reason for using Manyullyn instead of Cobalt.
If durability does not matter to you, just stick with Cobalt.
In Tinkers' Construct 1.7.1c (1.7.10 - this doesn't apply to 1.6), the flux modifier was changed to require "at least battery capacity/1000 in durability to be applicable." This is specified in the changelog.
If you have a cobalt pickaxe, you have to make the handle or axe head out of manyullin in order to use a hardened energy cell. The other tools have different thresholds - for instance, a cobalt hammer will accept a hardened energy cell.
Apart from durability, this is the only functional difference I'm aware of.
In my mind, there is no point to use manyullen other than weapons. Best pickaxe: cobalt head, paper binding, thaumium tool rod. Put a leadstone capacitor on, (higher grades don't improve RF storage), lapiz for fortune, max the rest out with redstone. If you build exactly that, and you add the: gold block + diamond, diamond block + notch golden apple, and nether star, you end up with a pickaxe with infinite durability and a mining speed of 53! For the energy, keep a capacitor in your hot-bar and you will never look back.