IMHO the alum does a better job on nicks but the WH is more soothing. Alum can burn a bit and give you feedback on your shave while WH does not burn. I usually use WH and only on occasion use the alum bloc. Some folks like the alum because they say it "tightens" their skin.
I used to use both, and I now only use the WH. I just flat out forgot to rub the alum on a couple of times and noticed that I felt at least as good as when I would rub it on, so I just dropped it from my routine. I still use an alum block to give me some grip and as a deodorant.
As far as feedback from my shave, my face already tells me all I need to know.
I use both, but if I could only go with one, I'd have to pick the alum since it stops irritation on my neck for me. It's a tough call though, witch hazel is good stuff.
I can honestly say I never used alum before. I'll break out the styptic pencil if I have a gusher, which stings A LOT lol. WH though feels great though
I'll also use alum if I have a minor incident, otherwise WH to finish. I also find alum can irritate my neck a bit, but it's usually a sign I've gone in too deep.
All I've had is witch hazel and styptic pencil.
But I was near an Indian market today so went in and came out with a smallish (3/4 x 1 3/4x 1 3/4 inches) generic alum block for $2.50.
Will give it try sometime soon.