I would say that there is no real difference.
Asset management companies that is part of large banking groups usually seat in separate entities and operate independently from the rest of the bank. Assuming proper procedures (and regulators usually check that) are in place they will not share information with the rest of the bank and their assets are clearly segregated from the rest of the bank. They have the same fiduciary duties as an independent AM and are probably using the broker/dealer services of other banks as well as their parent. Reputation is a key issue for banks and conflict of interests are usually managed properly.
Independence also comes and goes. The corporate history of Neuberger Berman is a good example. Neuberger Berman was once an independent asset manager. In 2003, it merged with Lehman Brothers, thus loosing its independence. When Lehman went bankrupt in 2008, NB did not join its parent company in bankruptcy and did not lose the assets of its clients. The company continued to operate until it was acquired by the management.
Finally it is mostly a question of marketing and positioning.
- Independent asset manager will put their independence forward as a key
selling point and as a proof that they cannot be conflicted.
- Asset management arms sitting within a larger group, will insist on the fact that they
offer a on turnkey solution for all that matters to an investor