The Problem with Red Mage . . .

[Neisan_Quetz]

Str Shikargar is better for most situations regardless of your main hand (the attack penalty is the only reason req sees a larger benefit, both ws benefit from fstr/attack boost from it). Eurus are unnecessary in the first place even at 25% (visible) haste.

The rest is just :/ There are very few pieces (in terms of equipment slots not main/sub) which even equal the benefits of Shikargar much less surpass it. You can't say fstr/attack provides a benefit to one and then downplay the benefit it gives the other.

EDIT: Eurus is better if you gain a full 1% haste from it, but not if you only get the partial percent from going from 25 (visible) to cap