UBS and Credit Suisse both have strong wealth management businesses — and the new year seems to have brought new hope.

UBS, which has written down more toxic assets than any other European bank, says it has had an “encouraging” start to 2009, with inflows into both its wealth and asset management businesses in January. Credit Suisse says it had a “strong start to 2009″ and was profitable across all its units so far this year.

This could be music to the ears of the Swiss, whose country may be faring better than others in the downturn (so far, at least) but is particularly reliant on its financial sector.

But we have heard this before, and not everyone is convinced.

Kepler Capital Markets’ Dirk Becker reckons a “horrific banking year” included an acceleration in the destruction of UBS’s core wealth management business in the fourth quarter. At Credit Suisse, “the results are weak, but not as devastating as UBS,” Becker says.

Even the banks don’t seem sure. UBS says it’s still cautious and financial market conditions remain fragile.

Credit Suisse CEO Brady Dougan admitted the bank made mistakes, adding: “This is not a light at the end of the tunnel message.”