I think you'll be happy with your Plumb (if it's sized big enough for an adult; some are; some aren't) At any rate it's a great collector's piece; in fact that in itself may detract a bit from your enjoyment using it; the fear of losing or damaging a favored collectible.
As I said I still have mine from 40 years ago when I was in the Scouts. I wish I had also kept the 3/4 Plumb axe but i gave it to a younger cousin when he went into the Scouts and I have no idea where it ended up.
But most of the axes I've used over the years were either no name or cheaper names like Collins. And I've used a lot. All of them were good axes TBH. The only reason I reccomended AGAINST the True Temper in you links was the one piece metal handle. True Termper is also a good brand, I just couldn't reccomend that model (and that's only my personal preference) As mac said, an axe is just a tool (and a fairly simple tool at that)