Hydrogen bonding in alcohols vs amines
Both reasons given are valid and contribut to alcohols having higher boiling points than amines, with one caveat. It is not stated whether the amine is primary, secondary or tertiary, and a tertiary amine has no $\ce{N-H}$ bond.  

Although the $\ce{O-H}$ bond is more polar than the $\ce{N-H}$ bond and can therefore form somewhat stronger hydrogen bonds, the fact that an alcohol has two lone pairs is the main reason for the higher boiling point.  

Even though a primary amine has two hydrogens that can act as hydrogen bond donors, their already weaker $\delta +$ is spread among two hydrogens, making those hydrogen bonds very weak, effectively limiting them to act as a single hydrogen bond donor.  

So, in general, an amine can only participate as a single hydrogen bond acceptor and donor (except for tertiary amines), while an alcohol's two lone pairs and single hydrogen allow for a much stronger hydrogen bonding network.