Heh, sorry I just like to keep everyone honest.
The explanation from your book is correct, I guess. I wouldn't call it a cross-conjugated system, but I suppose you could make that argument.
Cross conjugation occurs when you have two electron donating groups on opposite sides of a withdrawing group. In such a case you can only draw resonance structures that involve one of these donating groups at a time. Therefore, the competition between the two groups leads to overall a worse stabilization.
The explanation I would go for would be based more on the pKa difference between the two compounds. The one with a higher pKa would have less enol content.
The pKa explanation is a lot simpler, but I suppose the cross-conjugation explanation is more complete. The cross-conjugation effect is accounted for in the pKa, but not explicitly.