The common view in both Schools: freedom rooted in the intellect, formally in the will alone
To start here: when people ask which faculty free choice belongs to, a large share of the theologians of both schools hold that the freedom of human choice does in some way take its origin from reason and rests on the practical judgment's indetermination, or on a kind of self-action (αὐτοπραγία) in it, yet resides in the will alone as its subject.
The Schools put it this way: freedom is in the intellect only as its root, or as a cause without which it could not be, but it is formally in the will alone. On that view free choice is simply the will, whether insofar as it follows reason's judgment and dictate, or insofar as, among several means that reason points out, it takes one and refuses another, accepting this or not accepting it.
Latin
IV. Etenim, ut hinc ordiamur, quum quaeritur ad quam facultatem spectet liberum arbitrium, magna pars Theologorum tum hujus, tum illius Scholae, censet libertatem humani arbitrii a ratione quidem originem quodammodo ducere, & suum habere fundamentum in indeterminatione, sive in αὐτοπραγίᾳ quadam judicii practici; sed tamen illam voluntati soli, tanquam suo subjecto inesse; quod Scholae dicunt libertatem esse in intellectu radicaliter tantum, seu tanquam in causa sine qua non, sed formaliter in sola voluntate. Adeo ut liberum arbitrium non aliud sit quam voluntas, sive simpliciter quatenus rationis judicium & dictamen sequitur, sive quatenus inter plura media a ratione commonstrata unum eligit, alterum repudiat; hoc admittit, vel non admittit.