Cardiac MRI doesn't look at the coronary arteries directly (like CT), but is a functional test that assesses perfusion of the heart. Although there is no ionising radiation it does mean having an intravenous infusion, usually adenosine, as well as a simultaneous infusion of contrast medium. Asthma is a contraindication to adenosine, but otherwise it's a straightforward exam for most people.
It is usually considered in those with an intermediate pre-test probability of coronary artery disease or if the CTCA is non-diagnostic.
In general CTCA would be considered the first-line investigation in the UK for typical or atypical anginal chest pain, however in practice there is some variation depending on local expertise and availability.