You can claim income tax exemption on both house rent allowance (HRA) and repayment of housing loan. If you are living in a rented house and paying home loan on another property - even if both the properties are located in the same city - you can claim tax benefit.
Salaried individuals who live on rent can claim HRA to lower their taxes. It is partially exempted. However, if the individual does not live in a rented accommodation, HRA is fully taxable.