But the big societies are left behind by their smaller regional rivals (or other providers of financial products in certain cases), which continue to offer better deals across most areas.
The Which? report underlines the need for investors to keep checking the interest rates on their savings and how much they pay for other products. A family which selected a series of "best buys" tipped by the magazine - including savings accounts, house insurance, life cover, a credit card and pensions - would be better off by more than pounds 5,300 over five years compared with the average products on offer from the big banks and societies. Adding a Which?-selected mortgage, loan and overdraft over the same period would give pounds 1,000 further savings.
The report comes at a sensitive time for several larger societies, including the Halifax, Alliance & Leicester and Woolwich, which are planning to turn into publicly quoted banks later this year. The claimed benefits of flotation are that by offering an integrated set of products, the neo- banks are more competitive and cater more effectively for their clients' needs.
But critics of the move argue that banks offer worse deals because they must divert at least some of their profits into the pockets of shareholders. Some claim that even in the past year or so, since the big societies announced their de-mutualisation plans, they have been offering worse deals than their mutual counterparts.
The report in January's Which? compares different products offered by various banks and building societies over the past five years.
For Tessa savings schemes, Which? estimates that if savers had chosen the National Counties Building Society plan it tipped in May 1991 and invested the maximum pounds 9,000 allowed, the interest paid would have been pounds 3,109 - more than 20 per cent above the pounds 2,335 paid by Lloyds, the worst of the big banks. The Halifax, Woolwich and Nationwide, which paid out between pounds 2,817 and pounds 2,673, were marginally ahead of Abbey National, which became a bank in 1989. Barclays, NatWest and Midland lagged several hundred pounds behind the societies.
For instant access accounts, Which? assumed that savers with pounds 1,000 switched their accounts every six months or so to get the best rates. Had they done so, they would have earned pounds 395 interest over five years, mostly with small societies. Had they switched accounts but stayed with a single bank or building society, the total interest would have been just pounds 245 on average. Again, the Halifax, Abbey National, Woolwich and Nationwide - all present or former societies - head the table, paying between pounds 278 and pounds 249. Lloyds comes close, with pounds 245, while Barclays props up the list with pounds 187 paid over five years.
A similar picture applies with notice accounts. Investors who tucked away pounds 10,000 would have earned pounds 4,584 by following the Which? best advice list, usually from smaller building societies. Again, the Nationwide, Halifax and Woolwich came closest, paying between pounds 4,156 and pounds 3,944 to their savers. In contrast, staying with Lloyds would have earned pounds 3,499. Midland was the next worst, paying pounds 3,569, with Barclays, NatWest and Abbey National not far ahead.
However, while a similar picture emerged for mortgages, Midland was the surprise winner, beating the next best deal - offered by the Nationwide. Here, the survey assumed that borrowers were remortgaging last year with a new lender, having first taken out a pounds 50,000 loan in 1991. Researchers added the fees and redemption costs to the total interest paid since last year and found that since 1991, Midland borrowers would have paid pounds 18,914 in total costs, compared with Nationwide's pounds 18,914.
The most expensive home loans were with Lloyds and Barclays, both charging more than pounds 19,900.
The Which? report suggests that the life insurance arms launched by banks and societies in the past few years are hugely uncompetitive when set against life companies. A non-smoking couple, aged 30 and 29, who took out a joint pounds 50,000-a-year fixed-term assurance policy in 1991, would have saved pounds 363 after five years if they had opted for the cheapest cover with Albany Life.
Switching to the cheapest insurers for buildings cover on a pounds 67,000 property in Bath could have saved an average of pounds 217 on that charged by the big institutions, rising to pounds 278 in London. The Nationwide was the most expensive, followed by Lloyds, Midland and Barclays banks.
Contents insurance would have been pounds 154 cheaper in Bath and pounds 635 cheaper in London. In this instance, Lloyds was the cheapest of the big institutions, at almost half the price charged by NatWest.
Even with current accounts, traditionally an area in which the big banks have claimed supremacy, they tend to offer a worse deal, according to Which?. If you were overdrawn by an average of pounds 100 a month, you would have paid between pounds 33 and pounds 36 with the Woolwich, Nationwide and Abbey National, and pounds 95 with the Halifax. By contrast, charges at the Big Four banks ranged from pounds 278 at Lloyds to pounds 514 at NatWest. On an overdraft of pounds 500 a quarter, the banks would have charged from pounds 114 at Barclays to pounds 273 at NatWest, compared with fees of between pounds 28 and pounds 49 from the societies and Abbey National.