Stylistically...I think they are pretty different shoes (ofc this is said with a grain of salt...because a neophile that knows nothing about shoes won't know the difference).
The Hallam is your classic very CBD plain stich captoe oxford. The most versatile business dress shoe you can buy.
The Alex is your standard plain wholecut. Still CBD, still very dressy. Some will say that it is even more of a "formal dress shoe" than a plain stitch captoe. (You can even wear this shoe with a tuxedo).
I don't think you can go wrong with either a brown Hallam or a Black Alex.
With your wardrobe...I would buy a Black Alex first...then later on expand the collection into a brown Hallam.
Yes, I am leaning towards the black Alex for now. Or just get both.