Which of the resonance structures is more stable?
There are few things you should keep in mind while deciding comparative stability of resonance structures:

Non-polar structures are more stable than dipolar.

Resonance structures with a greater number of covalent bonds are more stable than those with lesser number. Thus, nonpolar structure of buta-1,3-diene is more stable than any other resonating structures.

Resonance structures with similar charges on adjacent atoms are insignificant due to electrostatic repulsion and thus are unstable.

Structures with positive charge on electropositive element and negative charge  on electronegative element are more stable.

Structures in which charge is delocalised are more stable than those in which there is charge separation.

Structures with complete octet are more stable.

All the atoms in a molecule taking part in resonance should be co-planar. because this enables effective overlap of p-orbitals and delocalization of electrons.


But when you have to decide among these properties itself, you can use the following observational facts:

Although during comaprison, there may be a positive charge on the more electronegative atom(O in this case) with complete octet, but it will be preferred over a structure with an electropositive atom ( C in this case ) having positive charge and incomplete octet.

But when number of covalent bonds are same, positive charge on C atom with incomplete octet is more preferred than positive charge on more electronegative O atom.

A stable neutral structure is a major contributor of a resonance hybrid.


An important note: when you are comparing the stability of the resonance structures , you are actually trying to figure out the major contributor to the resonance hybrid (that which best describes it). Technically, all the resonance structures are contributors to the same true structure of the ion. Since all of your mentioned structures represent the same species, they cannot have have different energies, and therefore they cannot have different stabilities.
Your question is actually asking &quot;which contributor is more important in describing the structure and behavior of the hybrid?&quot;
So fact number 1 and 2 makes it very clear that structure 4 in this case will be the most stable.