In Java when a final field is assigned a constant value compile-time, it usually makes sense declaring it static. It saves overhead according to the relevant PMD rule.
Does it make any sense or difference doing it in GWT regarding the generated Javascript code?
If the variable is assigned when it is declared final, then yes, static makes a certain amount of sense, but there are cases where it should not be static:
Another case: If the instance var is not a string or number constant, but requires running a constructor, that constructor may have side effects each time it is invoked, so running it only once is different than running it multiple times.
That said, GWT will inline/intern constant string values, so if you have multiple String fields all assigned to the same value, GWT will probably detect that and promote them all to static.
GWT will notice that this is never assigned except when declared, and may even remove the field itself.
The best rule is to start with the best (i.e. most readable, most maintainable, most efficient) Java code, and to only break from that in cases where GWT requires something specific. This is not one of those cases: the compiler should perform the same basic optimizations no matter how you write this.