Amongst Butan-2-ol and Butan-2,3 diol which has higher rate of dehydration?

The carbocation formed in Butan-2,3 diol is more stable as it will rearrange to get +M stability from alcohol group. However, the product will be aldehyde(due to tautomerisation ) for Butan-2,3 diol and alkene for Butan-2 ol.

As rate is determined by stability of carbocation, Butan-2,3 diol should have faster rate. Also the products don't give any extra hint. Right? But the answer given for higher rate is Butan-2-ol. Is there any point that I have missed out?