I own both, and have for some time, so I do have experience with them.
The Phoenix is the more-fun shooter. It holds ten rounds, has a crisp and consistent single-action trigger (that drops a real hammer, unlike the "other" Zamak-cheap-class pistol out there), and has a rear sight that is at least adjustable for windage. The guns weight is well balanced, too. I was very pleased when I got mine back in 2009, and remember feeling impressed with it right away. It's surprisingly accurate to where I've tried it.
That being said, the HP22A is complicated. It has two (yes, two!) manual safeties; the right combination of positioning is required to make the gun go bang (okay, pow.) In addition to those, there are three passive safeties. One requires the lower manual one (the trigger-blocker) to be engaged to remove the magazine (but it then has to be off to rack the slide. Imagine trying a quick reload under those requirements!) Another is the common mag-out safety, and the third locks the slide closed if there is no magazine in place (how are you then supposed to clear the chamber? You unload the magazine, re-insert it, put the lower safety off, rack the slide, put the lower safety back on, and remove the magazine again!)
The Taurus fills the hand even better than the Phoenix (my hand, anyway) with its thicker grip. It's a bit lighter than the HP22A, and holds eight rounds in its magazine. The DAO trigger has a long pull (which doubles as a safety feature; you're not gonna accidentally fire this gun.) Sights are rudimentary, a small front post visible through a cut in the rear sight, and not adjustable at all. Think self-defense sights, like those on a J-frame. The tip-up barrel aids loading and clearing, as you're not gonna be able to pull that thin, hard-to-grip slide back against the beefy, hammer-pounding mainspring and dual recoil springs (which are within the grips; that's why the grip is so, uh, robust.) I like DA/SA and DAO pistols, and trained a lot on them, so the PT22 trigger does not bother me at all. I found the gun pretty darn accurate with that trigger and those crude sights. I got mine, made in 1998, in 2012.
The Taurus also has the mag-out safety, and the mag-out chamber-lock. However, with the latter, you can still simply tip up the breech without a magazine in place to clear the gun. You also need not strip the Taurus to clean it because of that feature.
Were I to be picking between the two, I'd go with the Taurus. If I'd bought mine first, I'd never have bought the Phoenix. It doesn't sound like you're looking for a burn-up-hundreds-of-rounds-at-a-time plinker or range gun, and the PT22 can be fun in the casual sense you're alluding to. It can also double as a defense piece, since it can be carried loaded and ready to "pull, point, and press-to-play." There is a manual safety lever for those people (or jurisdictions) who require them, but I never use it. That heavy trigger is safety enough (again, like a J-frame.)
Both pistols, being the small, heavily-sprung rimfires that they are, do well on good-quality ammunition. I'm not dumb enough to run cheap, bulk-packed ammo in a tiny blowback and then complain the gun is a POS when it chokes a bit on it. I've only shot CCI MiniMags in the Phoenix, and only those and Federal AutoMatch in the Taurus. Have not had a malfunction with either load, in either gun.