The survey of 50,000 customers of CBA, NAB, ANZ and Westpac found that NAB had the highest share of its customers' superannuation business at 18.5 per cent.
Westpac came in second at 13.9 per cent, followed by CBA (13 per cent) and ANZ (11.6 per cent).
All four have found it difficult to difficult to crack their customers' superannuation, said the report – with all four showing "no real improvement" over the last decade.
Roy Morgan industry communications director Norman Morris said the big banks are facing tough competition from the trend to SMSFs, along with industry funds and other specialist superannuation providers.
"With funds in superannuation set to reach $2 trillion in the near future, super is likely to remain an important focus for the major banking groups if they are to retain their traditional position as their customers’ main financial institution," Mr Morris said.
When it comes to overall share of customers' wallet, CBA continues to lead at 34.2 per cent, Roy Morgan found.
NAB and Westpac both have the same share of wallet at 32.1 per cent, while ANZ has 28.8 per cent.
CBA has the leading share of wallet when it comes to accounts/deposits (60.3 per cent) and loans (56.4 per cent).
"Over the last decade, the big four banks have been making steady progress in obtaining a higher proportion of their customers’ business (share of wallet) for deposits and loans," Mr Morris said.
"However there is still a big opportunity for growth in both of these product areas as they are still only achieving around half of their customers’ business.
"This indicates a lack of loyalty to the major banks by their customers, probably due to a lack of incentive for them to consolidate and the need to spread the risk," Mr Morris said.
