Do you think that a regular half wave dipole cut for 2 meters hung vertically would be just as good as a J Pole at the same height even though the J Pole would be cut for a full wave ?
A J-pole is a half wave
radiator with a quarter wave matching stub.
In theory, the radiation pattern is exactly the same as that from a half
wave dipole, quarter wave ground plane with sloping radials, or any other
antenna that is about the same length.
In practice things are somewhat different due to the effect of the feedline.
A vertical half wave dipole works well if
the feedline can be kept from
affecting the pattern, for example, by side-mounting the antenna on a mast
using a stand-off with the feedline running away at right angles to the antenna.
If you just stick the dipole on top of the mast with the feedline running down
beside the lower element, that doesn't work as well. (One common commercial
solution is to bring the feedline down inside
the bottom half of the dipole.)
Similarly, a J-pole is prone to common mode currents on the feedline and/or
mast, because it isn't really a balanced antenna. These can affect the
radiation pattern: we put up one J-pole that couldn't hit the local repeater
until we insulated it from the support mast.
So both antennas are expected to have identical performance when properly
installed and decoupled. Both antennas may have degraded performance
when antenna currents flow anywhere other than the desired antenna