Why does depurination happen at a higher pH (or under less harsh conditions) than depyrimidation?
Really interesting question!
Mechanism of acid catalyzed hydrolysis of purine nucleosides is known to proceed through unimolecular departure of base moiety(DOI: 10.1021/ja00709a055).


It seems that someone else has also asked the same question: "Why reaction rate with pyrimidines is so much slower?" -and published paper of the reaction mechanism (DOI:10.1039/P29940000309). 

In the paper it is suggested that pyrimidines follow different reaction mechanims. This would explain huge differences in reaction rates. 


  In other words,
  the structure-reactivity correlations lend additional support to
  the previous suggestion, according to which the acid-catalysed
  hydrolysis of 4-oxopyrimidine nucleosides follows an openchain
  mechanism      


Open chain mechanims: