ASX bank stocks are being smashed again on Thursday.
At the time of writing, ANZ Group Holdings Ltd (ASX: ANZ) shares are down around 2% and changing hands at $33.96. The banking giant's shares are now down 17% from an all-time high recorded in mid-February, and 7% lower for the year to date.
National Australia Bank Ltd (ASX: NAB) shares are also down around 2% today, and trading at $35.69 at the time of writing. NAB shares are now down over 27% from an all-time high in late February and are around 16% lower for the year to date.
Many ASX 200 bank shares have slumped recently as concerns around the Federal Budget's property tax changes, higher interest rates, disappointing quarterly updates, and ongoing global volatility continue to spook investors. And many are rushing to sell up their holdings.
But when it comes to two of the big four banks, ANZ and NAB, there is one I'd sell and one I'd hold onto.
Here's why.

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I'd hold ANZ shares
ANZ was one of the few banking giants that actually posted a positive first-half FY26 update last month.
In early May, ANZ reported a 70% jump in its cash profit for the first half of FY26. Statutory profit was also up 62%, operating income was up 3%, and the bank's operating expenses were 22% lower.
The bank also confirmed it has now achieved 49% of its gross cost-savings target of $800 million for FY26.
It's clear that the bank has been working hard to reduce costs and simplify its operations, and its results last month suggest all its efforts have paid off.
If profit continues to grow, there could be a glimmer of hope ahead for ANZ shares over the next 12 months.
Brokers look to have become more positive on the stock, too.
TradingView data shows that half of its analysts (eight out of 16) have a hold rating on ANZ shares, but another six have a buy or strong buy rating.
The average $34.98 target price implies a potential 3% upside at the time of writing. But more bullish analysts think ANZ shares could climb 19% to a maximum target price of $40.50 over the next 12 months.
Citi is one of the more bullish brokers. The team has a buy rating on ANZ shares and a $40 price target.
UBS is slightly more bearish and rates ANZ shares as a hold. But its $36.50 price target is still higher than the average.
I'd sell NAB shares
NAB was one of the worst performers among the big four major banks last month. Its disappointing half-year FY26 results didn't help.
In early May, the bank posted a modest earnings growth, including a 6.4% increase in underlying profit and a 3.1% increase in revenue. But the results were a miss versus expectations, and investors weren't pleased.
Unlike ANZ, NAB's outlook is much less positive. The bank is facing continued headwinds over the next 12 months, including margin pressure and slower profit growth.
Weaker sentiment is shown in analyst outlooks, too.
TradingView data shows that 10 of 16 analysts have a hold rating on NAB shares. Another four rate the banking giant as a sell.
The average $37.53 target price currently implies a potential 5% upside at the time of writing. Although some think the shares could fall up to 19% to $29 each in the next 12 months.
Mark Gardner from MPC Markets said his team is bearish on NAB shares. He said they believe the bank's near-term earnings outlook is under pressure. The broker recently said that while its dividend remains attractive, valuation support is less convincing if earnings momentum continues softening. Gardner has a sell recommendation on NAB shares.
Catapult Wealth's Dylan Evans also has a sell recommendation on NAB shares. He said that recent changes announced in the Federal budget, coupled with households pressured by rising interest rates, could create new headwinds for the bank.