Tevar has less comparative studies than open repair. It was initially used for those who were poor surgical candidates. Tevar has a higher risk of endo leaking than open repair , but that said - The more done, the better the results. It is also much more country specific and even part of the country specific. Insurance Reimbursement will always be an issue. The techniques involved are excellent. I suspect it will be much like TAVR for aortic valve replacement, which is now more mainstream than open repair. Now, if you qualify for a TAVR it is the better approach to open repair.
Many centers monitor the TAA and wait for the aortic valve to need repair before prompted to open the chest and repair both. Like all surgical procedures, it is an evolving science.