First, I prefer a heavier caliber, generally more than needed. (either my rem bolt in 30/06 or G3 in 308). That said...
The last time I went hunting I took one deer with a 7.62x39 with soft point and one with the 308. The 7.62x39 was a botched shot on my part and it ran about 150 yards and required a follow-up shot (you botch a shot, it doesn't really matter that much, you've just created a bad situation for your prey). The 308 was spot on and it dropped where it stood.
My brother took 2 with a 223 using, iirc 62 grain soft points. Both ran about 30 yards and expired.
These were Texas deer, so pretty small.
I have been in the hunting party where 223 were used in about a half dozen instances. In EVERY case the deer was down as quickly as any other caliber used. This is personal experience only, ymmv.
My opinion is I would always choose a heavier caliber (243 or better in Texas), but if that's what I had (and it's legal) I would be fine with using it. (and I'm a meat hunter, respect the animal kind of guy.)