Absolute freedom to run away from danger, anything spawning, walking at you, even being spawned from your own deck, you've got a 0-cost trick up your sleeve to just, walk away, at not resource cost.
I always liked Think on Your Feet, this version just supercharges the strength of the original and adds an icon on top to fuel some archery or evasion. The strategy options are useful, duck a foe without spending actions, net a bonus move to faster get to a location, evade a threat while you aren't equipped to deal with it. The card is stronger in a larger scenario or a particularly small one, where the limited or expansive space is supposed to be a challenge to navigate. The added maneuvering speed is good, especially if you have lots of actions already via Leo De Luca, you can distance yourself from a hunter or focus on those clues or equip that weapon you need to kill the thing you just got away from.
The specific advantage to the upgrade over the basic version is the ability to now automatically duck from enemies who are moving. Say a hunter is sitting on a location with clues, or some kind of boss is getting in the way, suddenly their movement becomes an opportunity for you to get at the locations they occupied quickly, a switcheroo!!
Whatever the specific use you'll find for it, Think on Your Feet will probably not disappoint, but keep in mind that there is an art to when and when NOT to use it. Save it for a moment where the movement and/or escape is guaranteed to be useful, not before.