Most have given you a lot of practical differences for both barrel length's.
The shorter barrel may be a tad more accurate than the 23" due to rigidity, so any velocity loss may be made up for in getting the round more centered in the vitals at distance. The velocity drop per inch of lost will be dependent on the rifles own expansion ratio and the many bullet/powder type and charge weight combinations. There is no fixed number, except in a given rifle with a given load and the actual barrel chopped inch by inch, and then even this will vary from longest to shortest with that one load.
Some remind you of the extra muzzle blast and this can be an issue with large powder charges like in the 416 uncorking at high pressures. Ka-boom........ba!! Some rifle cartridges become down right nasty when they get too short.
Another consideration and this is a small one, but worth mentioning because it is important to me is the appearance.
Does the tube length balance with the fore-ends length?
Some rifles look better with rifle length barrels, while others are more beautiful with 20" carbine lengths or shorter.
Sometimes if the same overall length stock is used, some carbines look kinda funny with a long forearm. I usually go for the shorter barrel, however as I said some rifles are not as appealing with carbine barrels and nothing else made more compact to balance it all.
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Take a Model 70 featherweight. The 22" tube and the standard length Schnabel fore end are a match made in
Haven, New Haven to be exact.

If you cut the barrel to 20" now something looks wrong. If you take the newer M70 compact with it's 20"bbl and downsized stock, then all is well.
I had the M70 lightweight sporter with the 22" tube in .30-06. This rifle looked unbalanced because of the shorter fore end compared to the Featherweight's fore end. It would have been more balanced with a 20" barrel, as such they were called light weight carbines.
An M-14 rifle is a beautiful balance with a 22" barrel. A 18.5" carbine looks to be bubba'ed to me, and again only for a balance to the looks, not to functionality or lethality itself.
Didn't want to bore you with appearance themes, but you know, we all like the look of our guns, so really look closely at both barrel lengths to see what you will really love to handle each hunt, the other mechanics are probably a lesser concern in the big scheme of things.