Which one has higher priority according to Cahn–Ingold–Prelog rules?
You are correct. In both cases $\ce{CH2OH}$ has higher priority. the Cahn-Ingold-Prelog system uses atomic number as its primary determinant of priority. However, a popular misconception is that the CIP system uses something related to "size", like mass, number of carbon atoms, length of chain, etc. 

Here is a way that I use when I teach the subject. In the following compound, the chirality center has two bonds to carbon atoms. The carbon atom on the left is bonded two an oxygen atom and two hydrogen atoms. The carbon atom on the right has two bonds to another carbon atom and one bond to a hydrogen atom. Write these connections vertically below the carbon atoms with highest atomic number at the top. Compare each row, and the first difference is where you judge. In this case, the first difference is the first row: oxygen has a higher atomic number than carbon. $\ce{CH2OH}$ has higher priority than $\ce{CH=CH2}$.



You can do the same analysis for $\ce{CH2OH}$ vs. $\ce{C(CH3)3}$.