For bench shooting they can both shine..Each has it's own merits and each has their own preferences for being a bench gun. The 223 will be easier on the shoulder to shoot,and cheaper to reload for,and most likely easier to set up for. Both have a excellent choice of quality components to choose from.Both can be exceedingly accurate.
Things to ask yourself before deciding..
What range am I going to shoot.. I know you have said earlier that 200 Yards was your self imposed limit for hunting ..do you plan on increasing this distance for bench shotting? If not..then no questions about it..go with the 223 bull barrel..and IMHO.. get one of the 24" ones. Having a dedicated Handi bench gun and striving to make it shoot in the 1's & 2's consistently is not an easy task..Not only do you have to prep the gun to be able to shoot those kind of groups..but you have to train yourself to be able to shoot them on a regular basis,so..Am I willing to do what is needed to accomplish this? Shooting and loading for this is more involved than just shooting for casual groups or sighting in for deer hunting.
If you are wanting to stretch the distance out to and beyond 300 yards..then get the 243 bull barrel. The ballistics of the 6mm's will outshine those of the 22's when dealing with any wind you will encounter at long ranges. Again..IMHO get either of the 24" bull barrels. The reason I say go with the longer barrel is simply..more velocity..in bench shooting this something you want to have at your disposal. You will be working up loads finding which works best and at what velocity..
There are a lot of people who dislike the 243's in the Handi's..most of them I have found don't take the needed steps in their fitting,reloading or barrel bedding process to make these rifles truly shine,which is why you will see the 223 get recommended more often than the 243.It's just a lot easier to get them to shoot good.For a truly dedicated bench rifle..each will have to have it's own forearm and bedded properly for it.If you just want an occasional bench gun that shoots good..then that is different.The 243 can be very picky in this regard but once you have it figured out,then you can reap the advantages it offers.
Either one..for a bench gun..have the factory fit it for you.I have always included a nice note to the gunsmith taped to the reciver thanking him for taking his time to fit the barrel perfectly and tuning the trigger for me to the lowest safe pull he was allowed to do for me.A perfectly fitted factor barrel starting off with a 3lb. trigger pull will make having what you want 10x easier than one you are unsure of and have to tinker with to get right no matter which barrel you elect to go with.
If you don't believe the 243 is used in matches..then you haven't really looked into it..Go here..this will give you a better view of what the 243 offers to those who choose to use it.
http://www.6mmbr.com/243Win.htmlGood Luck
Mac