What is the difference between the V-shape tail and the straight tail on the Beechcraft Bonanza?
V-tails have been fashionable in the Fourties and Fifties, and the claim was that they would cause less drag than an equally effective conventional tail. This has two reasons:


Average chord length is longer, so the Reynolds number of the airflow is higher, causing relatively less friction drag.
Instead of three surface-fuselage-joints, the V-tail has only two, so less interference drag is created.


Flight testing of V-tails showed only marginal advantages, and in damping they are less effective than a conventional tail which is dimensioned for the same control effectiveness. The control effectiveness of a control surface is proportional to the cosine of the V-angle, but the damping characteristics go down with the square of the cosine.

@nimbusgb mentions the tendency of the V-tailed Bonanza to fishtail: That is a consequence of too little lateral damping.

Also, when a combined elevator-rudder input is commanded, the V-tail will produce a very high deflection on one side, while the two commands will cancel out on the other side. This will reduce overall control power in cases where a combined elevator-rudder input is commanded over what is possible with a conventional tail.

Even the glider designers, who had enthusiastically tried out V-tails, have now returned to conventional tails (more precisely, T-tails) because the expected benefits did not materialize. And glider designers will try anything to improve the aerodynamic quality of their designs.