Thermi vs Profound RF for breasts?

Great question and probably no wrong answer.  There are several variables to consider cause one inch lift is NO SMALL ASK when it comes to non cutting breast reduction/tightening!  Depending on your age, your doctor may ask you to get a mammogram or breast US before the procedure.
If you have smaller, lighter weight breasts, then Profound, whose RF micro-needling, tightening effect is isolated to the skin and immediate sub-cutaneous tissue is a great choice and slightly less invasive.  We use Profound on faces, necks, upper arms, thinner inner or lower thighs etc, where the skin is generally thinner.  It's not great for thicker or weighted tissue.
Alternatively, if the breasts are more pendulous and heavy, the ThermiRF (or the newest model - "Arvati" that we have) is a better choice for tightening the ligaments in the breast, glandular tissue and dermis, sometimes after some conservative lipo - mainly of side and bottom breast tissue, to maintain cleavage and upper pole fullness.  Thermi uses a 20cm long, tiny, blunt, insulated cannula that is introduced into the numbed tissues through a tiny incision in the anterior armpit crease, and sometimes the infra-mammary fold or even the areola on each side. The temperature is precisely monitored inside and out in order to protect the epidermis from getting full thickness burns while causing maximal treatment in the under lying tissue.  Now, if your exam is in between, and your doc has both technologies, you might consider both, as they complement each other and maximize the effect you are seeking.  Obviously that costs more because both technologies use expensive disposable, single use, single patient applicators and it would take nearly twice as long to do.
I hope that helps and that you get a great outcome!
Best, Z