For this question, given the lack of initial information, I'm making the following assumptions:

• Butane-2,3-diol dehydrates to give butan-2-one
• 2-butanol dehydrates to give but-2-ene

Butane-2,3-diol dehydration is nicely described in this paper from Emerson¹:

Aqueous 2,3-butanediol was shown to react in a pseudo-first-order reaction in the presence of sulfuric acid to form methyl ethyl ketone. The reaction could be described by a pinacol rearrangement mechanism and had an activation energy of 36 kcal/mol.

Finding the data for dehydration of 2-butanol proved more elusive. One study² conducted dehydration rate experiments for secondary alcohols at $250^\circ \text{C}$ and 40 bar pressure and obtained a rate constant for 3-hexanol to be $k = \pu{ 0.067 \pm 0.021 hr^{-1}}$. Assuming this rate would be similar to 2-butanol, we can find the activation energy via the arrhenius equation, which comes out to be around 48 kJ/mol, which is around 11.52 kcal/mol. Another source³ conducted the same experiment over a copper-chromite catalyst, and obtained an activation energy of 13 kcal/mol. This means that 2-butanol will dehydrate faster than butane-2,3-diol.

From a conceptual standpoint, this makes sense: The pinacol rearrangement mechanism would require a hydride shift, which would be the RDS and would take more time and energy than a simple carbocation formation. However, if you're comparing absolute reaction rates, a large number of factors come into play, and given the right conditions, butane-2,3-diol can dehydrate faster than butan-2-ol.

References:

1. Emerson, Richard R., et al. “Kinetics of Dehydration of Aqueous 2,3-Butanediol to Methyl Ethyl Ketone.” Industrial & Engineering Chemistry Product Research and Development, vol. 21, no. 3, 1982, pp. 473–77. doi:10.1021/i300007a025
2. Bockisch, Christiana, et al. “Kinetics and Mechanisms of Dehydration of Secondary Alcohols Under Hydrothermal Conditions.” ACS Earth and Space Chemistry, vol. 2, no. 8, 2018, pp. 821–32. doi:10.1021/acsearthspacechem.8b00030.
3. Joseph Sires Cantrell, "Rate and activation energy of the first order dehydration of 2-butanol over a copper chromite catalyst", 1954, source

For this question, given the lack of initial information, I'm making the following assumptions:

• Butane-2,3-diol dehydrates to give butan-2-one
• 2-butanol dehydrates to give but-2-ene

Butane-2,3-diol dehydration is nicely described in this paper from Emerson¹:

Aqueous 2,3-butanediol was shown to react in a pseudo-first-order reaction in the presence of sulfuric acid to form methyl ethyl ketone. The reaction could be described by a pinacol rearrangement mechanism and had an activation energy of 36 kcal/mol.

Finding the data for dehydration of 2-butanol proved more elusive. One study² conducted dehydration rate experiments for secondary alcohols at 250 °C and 40 bar pressure and obtained a rate constant for 3-hexanol to be $k = \pu{(0.067 \pm 0.021) h^{-1}}$. Assuming this rate would be similar to 2-butanol, we can find the activation energy via the arrhenius equation, which comes out to be around 48 kJ/mol, which is around 11.52 kcal/mol. Another source³ conducted the same experiment over a copper-chromite catalyst, and obtained an activation energy of 13 kcal/mol. This means that 2-butanol will dehydrate faster than butane-2,3-diol.

From a conceptual standpoint, this makes sense: The pinacol rearrangement mechanism would require a hydride shift, which would be the RDS and would take more time and energy than a simple carbocation formation. However, if you're comparing absolute reaction rates, a large number of factors come into play, and given the right conditions, butane-2,3-diol can dehydrate faster than butan-2-ol.

References:

1. Emerson, Richard R., et al. “Kinetics of Dehydration of Aqueous 2,3-Butanediol to Methyl Ethyl Ketone.” Industrial & Engineering Chemistry Product Research and Development, vol. 21, no. 3, 1982, pp. 473–77. doi:10.1021/i300007a025
2. Bockisch, Christiana, et al. “Kinetics and Mechanisms of Dehydration of Secondary Alcohols Under Hydrothermal Conditions.” ACS Earth and Space Chemistry, vol. 2, no. 8, 2018, pp. 821–32. doi:10.1021/acsearthspacechem.8b00030.
3. Joseph Sires Cantrell, "Rate and activation energy of the first order dehydration of 2-butanol over a copper chromite catalyst", 1954, source