I think that the question can be reduced to: is it easier to prove that something exists or to prove that something does not exist.
The argument in favour of proving that something exists is that it's easy to construct things that might satisfy the requirements and it's also easy to check if they indeed satisfy them.
In some cases this is true: if you want to find the root of a polynomial, it's easy to construct numbers and it's easy to check if they are roots.
The problem, of course, is that you have to be lucky. You might be able to reduce the search space, e.g. by proving that it must be a multiple of 5 or between 1 and 10; but, unless you limit it to a finite set of numbers (in which case you are not really using the "guess and validate" method), you don't have a method for solving the problem: you only have a method that, assuming you are extremely lucky, might generate a solution.
But if you want that, it's equally easy to prove that something does not exist! Generate texts that could be possible solutions and check if they actually are.
Therefore, having a method that might yield the solution by pure luck does not mean that proving that something exists is easier.
Now, is it generally easier to prove that something exists with some other method? It depends on the actual problem because otherwise proving that something does not exist would be reduced to proving that a proof that it doesn't exist exists. And I'm afraid that we cannot measure that as there never was something that was proven to both exist and not exist so we can (attempt to) measure the difficulty of the proof.