As for enchanted underarmor/clothing, this is a fully customized set designed for Matou Shinji in his current form that can be worn in broad daylight / under a set of robes or outerwear. Compared to the Illuminati outfit, it lacks flexibility in that it cannot be reprogrammed later, and only boosts two attributes to a substantial degree (e.g. speed, might, vitality, emission control, etc).
...however, the magnitude of these boosts is rather higher than you'd get out of the basic agent armor, as it has no need to be flexible.
In addition, by default, the outfit includes gloves and socks made of salamander skin and otherwise is created from materials from an earth elemental, ensuring that Shinji is never without a Mystic Code when he is wearing the outfit (amplifies earth and fire-based spellpower and control)