What would make guanidinium ions and urea more effective denaturants of proteins in some cases, but not in others?
Chaotropic agents increase the solubility of nonpolar substances in
  water. Consequently, their effectiveness as denaturing agents stems
  from their ability to disrupt hydrophobic interactions, although the
  manner in which they do so is not well understood. Conversely, those
  substances  that stabilise proteins strengthen hydrophobic forces,
  thus increasing the tendency of water to expel proteins. This accounts
  for the correlation between the abilities of an ion to stabilize
  proteins and to salt them out. 
  1


Among other well established chaotropic agents, guanidinium ion ($\ce{Gu+}$) and the nonionic urea, which, in concentrations in the range 5 to 10 M, are the most commonly used protein denaturants. The effect of the various ions on proteins is largely cumulative: $\ce{GuSCN}$ is a much more potent denaturant than the often used $\ce{GuCl}$, whereas $\ce{Gu2SO4}$ stabilizes protein structures.



There are factors which have been investigated to explain why these two chaotropes appear to be effective in different cases (i.e they tend to be effective in some cases but not others). In one experimental investigation, the mechanistic basis of thermodynamic destabilisation due to urea and guanidinium was tested in order to find possibility that they exert their denaturing effect through peptide group hydrogen bonding (done experimentally by measurement of acid and base catalysed hydrogen exchange (HX) in a small peptide model)[2]


Urea


It has been established that urea increases the acid catalysed rate and decreases the base catalysed rate.


The acid catalysed HX rate in urea solution is higher than in the absence of urea. This can be expected when it is understood that acid catalysed HX proceeds dominantly through transient protonation of the peptide carbonyl group and deprotonation of the peptide NH by water or another base like urea and thus the proposed explanation is that urea forms an H-bond to the peptide carbonyl.[2]
In the case of base catalysed HX rate, which strongly decreases upon urea, the peptide NH group transfers its proton to a transiently H-bonded hydroxide. If urea is H-bonded to the peptide N-H, hydroxide can’t access the proton and HX is blocked.[2]


Guanidinium

With gaunidinium, as explained above, the effect of the various ions on proteins varies by some margin as they exert differently on the ion. It doesn’t selectively H-bonds to the peptide group (base catalysis) because guanidinium cannot H-bond to the peptide NH. Instead studies seem to suggest that guanidinium tends to engage in transient interactions with itself.[2]
Guanidium is often found to be approximately twice as efficient as urea in denaturing proteins but this varies with protein target. Helical peptide studies show that gaunidinium can be up to four times more efficient than urea when planar amino acids are major contributors to the helical stability. In contrast, guanidinium is barely more efficient if stabilisation is due to salt bridges. Thus protein targets are major contributing factor to the varying efficiency of guanidinium in denaturing proteins.[2]




Tl;dr

From above discussion, the varying effeciences depend on things like:


acid/base environment
nature of ions (the case of guanidinium)
protein target (e.g planar amino acids in helical peptides)




References


Voet and Voet Biochemistry. Section 7-1. Primary Structure Determination of Proteins.
Urea, but not guanidinium, destabilises proteins by forming hydrogen bonds to the peptide group. Woon Ki Lim 2595-2600 vol 106 no 8.