The Big Freeze based on the Lambda Cold Dark Matter theory, is the leading theory and the other two are just speculative ideas. The Lambda model describes a universe that expands forever but does not overcome local gravity. This means our Local Group of 54 galaxies, which are gravitationally bound, will ride the expansion wave forever. In essence, there is no reasonable end of the universe as we know it, but we do end in a Big Freeze eventually.
The Big Rip says the expansion wave will overcome gravity, eventually ripping everything apart including the strong force at the center of atoms. In this idea, the universe ends up filled with a diffuse cloud of particles expanding from each other, forever. This too ends in a Big Freeze eventually.
In contrast, the Big Crunch says that gravity will eventually win out over the expansion wave, collapsing the universe in on itself. In this idea, the universe might end with another singularity or perhaps a cyclical “bounce,” where everything passes through each other starting another expansion, a Cosmocycle if you will. Finally, while current observations support the Lambda model, the other two ideas have not been fully ruled out yet.