(Dow Jones) Among the details that Congress must now resolve in its push for broad financial reform is one of special interest to many of the country's richest families.

  The issue at stake: Will they still be allowed to manage their wealth in private or be pushed under government oversight and public scrutiny?

  The reform bill passed Friday by the Senate lets stand a 70-year-old exemption of family offices--noncommercial entities that provide investment-management, governance and sometimes concierge services to families with hundreds of millions of dollars--from oversight by the Securities and Exchange Commission. That exemption under the Investment Advisers Act applies only as long as the office caters to the lineal descendants of a founder and has fewer than 15 clients. (A "client" can be more than one individual and more than one trust or charitable entity).

  But House legislation passed late last year calls for family offices to register with the SEC as investment advisors.

  Now, differences between the two bills will have to be hashed out in a joint Senate and House conference committee--and no one's taking bets on the outcome for family offices.

  "It could go either way," says Karen Yates, a family-office specialist and a partner of the law firm Withers LLP.

  Family offices number a few thousand in the U.S. and account for around $1 trillion in assets, according to wealth-industry estimates. One bona fide, noncommercial family office made an unusual splash last week when billionaire TV and publishing magnate Oprah Winfrey established it to manage her personal investments, but most keep a very low profile.

  Those that do get most of the attention aren't family offices in the strictest sense. Firms like Rockefeller Financial, Bessemer Trust, and Pitcairn started out as private family-only outfits but became commercial multiclient businesses--in structure registered investment advisers or trust companies--in the 1970s and 1980s.

  Though the largest single-family offices are small by finance-industry standards, Yates says some House legislators are worried that family offices could be used as fronts for unregistered commercial activity. This stems from a common family-office practice of letting people other than the direct descendants of the founder--spouses, ex-spouses, in-laws and family-office employees--invest along with the family.

  Arguments can be made for counting relatives by marriage (or divorce) as family-office clients, but "including trusted employees makes the government very nervous," says Yates.