Is this for a receive application? Or is it transceive?
I have played with longer dipoles, full wave and longer than that. In general, I see little reason to go with a full wave dipole over other types of antennas. Particularly so if you are going to feed it with coax.
A half wave dipole exhibits a slight null off each end, but a broad beam perpendicular to the element. The classic broad toroid (doughnut shaped) radiation pattern. Pretty predictable and easy to visualize while setting the antenna up. The full wave dipole, or two half waves, has a couple dB gain over the half wave dipole, but at a cost.
There ain’t no such thing as a free lunch, so that slight gain has to come from a changed pattern shape. What I have found is that the full wave dipoles I have built exhibit a bit of a null perpendicular to the element, and a bit more gain at an angle. Think of it as a roughly butterfly shaped pattern, a null at each end and a slight null on the broadside.
I have found it harder, compared to other wire antennas, to place full wave dipoles in orientations that take advantage of the pattern shape. For example, a terminated long wire (a beverage) of the same length works, roughly, in a cone towards the terminated end, and I have found it easier to place them, for example allowing one lobe to point towards the polar path, while the other is towards Africa, or something like that.
And then there is the operational bandwidth. In my experience dipoles fed with coax (and with or without a balun) tend to be narrower banded than the same lengths end fed with coax and a balun. But, a full wave dipole fed with ladder is more forgiving.
I guess the question comes down to what do you hope to gain with the full wave dipole, vs a half wave dipole, that cannot be done with an end fed full wave?
If you are looking for a little gain, what direction / directions are you looking for gain? If you are looking for gain in specific directions, have you considered a V-beam or something like that?
T!