I read about the above mentioned theories then used them to predict the molecular geometry. However, I found that the shape/geometry of a molecule obtained from both the theories was same. For example, water has bent/angular shape according to VSEPR theory as well as Valence Bond Theory. So I wonder if there's any difference between the two theories in predicting molecular geometry.
Do these two theories ever yield different results?
VSEPR theory is a purely observational model, based on empirical knowledge. Many of the "rules" were added to fit the theory to what has been observed. It has quite a lot limitations and may only provide an initial guess for the structure of a molecule.
According to VSEPR, the structure of water is bent. While we would expect $\angle^\mathrm{theo}_\mathrm{bond}(\ce{HOH})=109.5^\circ$, it is indeed smaller $\angle^\mathrm{expt}_\mathrm{bond}(\ce{HOH})=104.5^\circ$. This discrepancy is explained with the reasoning that lone pairs require more space. This is wrong, and a caveat added to make the theory fit.
It would also predict the lone pairs of water to be equivalent. A statement which has experimentally been disproved. Quoting myself:
One popular example is water. In many texts the central oxygen is described as having (approximately) four sp3 orbitals, which essentially makes the lone pairs equivalent. That view, however, is not in agreement with the photoelectron spectrum, which clearly shows that the lone pairs are not equivalent. At this point I'd like to refer you to Michael Laing's article: "No rabbit ears on water. The structure of the water molecule: What should we tell the students?" (J. Chem. Educ. 1987, 64 (2), 124.).
The theory sometimes predicts correct structures, but that has no theoretical foundation. It is basically educated guessing.
When it comes to more complicated molecules, for example hyper-coordinated compounds like $\ce{IF7}$, most explanations (the involvement of d orbitals) break completely down and have been disproved many times. However, just by minimising the inter-ligand distances, it yield approximately the correct shape. This is a nice coincidence.
Valence Bond theory is on the other hand a highly sophisticated and complex approach, deeply rooted in theory. If applied at a modern, computational level, it will always yield the correct molecular geometry for the correct reasons (within its other approximations).
While we can approximately use a piece of paper and a pencil to do these calculations for simple molecules, it really is an approach at formulating a wave function and approximately solving the electronic Schrödinger equation. That requires a lot of maths and integral solving. It is not so much a theory that can be done on-the-go.
As it is such an extensive and accurate theory, it is complementary to molecular orbital theory. That means that they will yield the same results at their respective accurate (infinite) expansions.
For the example of water, VB theory would predict a bent structure. It would also predict non-equivalent lone-pairs, which agrees nicely with the photoelectron spectrum.
In conclusion; A sad fact is that both theories, VSEPR and VB, are usually (more than just often) taught completely wrong at below university levels (sometimes even there) and will introduce many artefacts into young scientists brains. Your statement, that you "used" valence bond theory is a reminder of that.
These theories could not be more different from each other. In most cases they predict structure on completely different grounds. It is basically a coincidence if they predict the same thing.
Take home message: VSEPR theory is a rule of thumb, VB theory is an accurate description of physics (within its approximations).
