I have had a couple Winchester takedown rifles, each over 100 years old, and they have still been tight and just as accurate as the solid frames. I just checked a target from my 111 year-old Winchester 1894 30 W.C.F. It was a 10 shot group of 2 & 7/8″ at 100 yards using cast bullets at 2,029 fps, with 7 of them going into a 1 & 7/8″ circle. With jacketed bullets, it would likely do even better.

I dont think takedown rifles shoot any less accurate than any other standard frame rifle (all factors being equal), even if they have a little play at the takedown (sights are on the barrel and point of aim wont be affected).  Ive shot several that had a little wobble to them but didnt affect accuracy.  Now if you have a takedown with some play in it and using a tang sight or receiver sight your point of aim may be moved or your shooting could be inconsistent.