An angiogram (in and of itself) is a diagnostic test, not a treatment method. The study you are referring to, nicknamed COURAGE, compared medications and stents (a treatment that can be performed at the same time as an angiogram) in a very limited population with stable coronary artery disease. Just because they found medication and stents essentially equal in morbidity in that population does NOT mean they are equal for everyone with CAD. (Nor did it address whether quality of life was "equal"...the results of that part of the study are still pending).
The first question I have is why does your doctor want to perform the angiogram? If it is primarily for diagnostic purposes, then you should probably listen to him. If he thinks he will want to place a stent while he is in there diagnosing, then talk to him/her beforehand about the study and why you are (or more likely are not) like the study population.
The study compared people on "optimal" CAD medications (e.g. beta-blockers, aspirin, and statins*) who had stable CAD (but NOT certain kinds/locations of blockages like the left main artery and a whole host of other types or complications of coronary disease...they screened more than 35,000 people with heart disease to get to the 1,100+ who were in each group) to those who had stents. Most of the participants had bare metal stents and did not take Plavix for more than about 30 days.
*Everyone received aspirin 81 to 325 mg/day (or Plavix if they had aspirin intolerance). Anti-ischemic therapy included long-acting metoprolol, amlodipine, and isosorbide mononitrate "alone or in combination" along with either lisinopril or losartan. For the cholesterol lowering meds, they used simvastatin alone or in combination with ezetimibe to get LDL down to 60 to 85. If HDL was still below 40 and triglycerides above 150, they then added exercise, extended-release niacin, or fibrates "alone or in combination."
The NEJM editorial, published in the same issue as the COURAGE study, concluded "Secondary prevention has proved its worth, with lipid-modulating therapy, lifestyle modification, and the use of aspirin, beta-blockers, and ACE inhibitors [but] patients whose condition is clinically unstable, who have left main coronary artery disease, or in whom medical therapy has failed to control symptoms remain candidates for revascularization..."