How large is the energy difference between keto- and enol-form of guanine and uracil?
I am not an expert in the field, but a quick literature check turns up a good amount of papers on the topic. In particular, I found this paper [1] which nicely answers the question for guanine:





So, in the gas phase, the most stable enol tautomer has a 0.9 kcal/mol free energy difference with the most stable keto tautomer. That free energy difference is very exacerbated in aqueous solution, with now a ∆G° = 8.7 kcal/mol. We also notice that the most stable keto tautomer is not the same in the gas phase and in solution, and that both keto and enol have many tautomers close in free energy, showing the limits of the simple keto vs. enol line of thought.



Regarding uracil, the first reference that comes up in a bibliographic search is this paper [2]. I only quote the abstract:


  The effects of the solvent on the tautomeric equilibria of cytosine and uracil are studied using Onsager's reaction field model in the framework of density functional theory. […] Our results are in good agreement with available experimental results and confirm that the polarization of the solute by the continuum has important effects on the absolute and relative solvation energies.





pKa Values of Guanine in Water: Density Functional Theory Calculations Combined with Poisson-Boltzmann Continuum-Solvation Model, Y. H. Jang et al., J. Phys. Chem. B 2003, DOI: 10.1021/jp020774x
Solvent effects in density functional calculations of uracil and cytosine tautomerism, L. Paglieri et al, Quantum Chem., 2004, DOI: 10.1002/qua.560560517