What is the best imaging technology for measuring damage to the heart muscle and vasculature. CT or MRI?

Many different tests. You need a good physician to check and guide you in case you have vascular(Coronary artery disease).
If you have risk factors for heart disease(such as smoking, high BP, diabetes or high cholesterol), then a stress test or nuclear stress test is best test. CT scan has some but limited value(to detect Coronary calcium). Echocardiogram is the best test to check the damage to the heart muscle.

Related Questions

EKG showed 'hardening' of heart muscle. Just had a SV Ischemia show on CT scan. Is this connected? Does Arrythmia cause the hardening?

Not sure . Not sure how an ECG can show hardening of heart muscle. It could show signs that may be related to previous damage of heart muscle. Damage of heart muscle can cause arrhythmia. Most arrhythmias, unless left uncontrolled for long periods of time do dot cause heart damage. . Read more...

What type of exercise is best for the heart muscle?

Aerobic. The aha recommends 150 minutes / week of moderate aerobic activity spread over 4-6 days for optimal cardiovascular health. Read more...