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

The carbocation formed in butane-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 tautomerism) for butane-2,3-diol and alkene for butan-2-ol.

As rate is determined by stability of carbocation, butane-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?