Investors view both National Australia Bank Ltd (ASX: NAB) shares and Commonwealth Bank of Australia (ASX: CBA) shares as dividend shares that pay appealing passive income.

However, as similar businesses, we don't need to own shares in both banks unless we're indirectly invested through an exchange-traded fund (ETF) such as Vanguard Australian Shares Index ETF (ASX: VAS) or BetaShares Australia 200 ETF (ASX: A200).

So, how would income-seeking investors go about picking one over the other?

To decide which ASX bank share I'd buy, I'd want to look at three factors: the size of the dividend yield, the potential size of dividend payments in the years ahead, and the sustainability of the dividend.

Let's explore.

Dividend yield

Dividend yields are similar to the interest rate a bank savings account pays. However, unlike a term deposit, dividends are not guaranteed and can be cut.

Let's look at the dividend yields for FY25 because that's the current financial year for both of these companies.

According to the independent forecasts on Commsec, CBA shareholders are predicted to receive an annual dividend per share of $4.95 in the 2025 financial year. That would translate into a grossed-up (including franking credits) dividend yield of approximately 5%.

The projection on Commsec suggests that owners of NAB shares could receive an annual dividend per share of $1.75 in FY25, which would represent a grossed-up dividend yield of 6.4%.

The future yields aren't hugely different, but I'd say NAB is the winner on the pure size of the yield, owing to its lower price/earnings (P/E) ratio.

Future payments

The board of a company decides how much dividend to declare, depending on factors like the health of the balance sheet, profit generation, the wider economic environment and outlook.

We can't know what the directors are thinking, but if future profits are expected to rise, then it's quite likely that the dividend can grow, too.

We can refer to profit estimates by the broker UBS to consider where the earnings of these ASX bank shares may go in the coming years.

UBS has forecast that CBA could generate earnings per share (EPS) of $5.99 in FY25 and this could grow 8.5% to $6.50 by FY28.

The situation could be more appealing for owners of NAB shares. UBS predicts that NAB could make EPS of $2.23 in FY25 and grow by 19% to $2.58 by the 2028 financial year.

If both banks continued with the same dividend payout ratios, then NAB's dividend income would grow at a faster rate than CBA's.

Passive income sustainability

I believe the dividend payout ratio is one of the most important factors for an ASX dividend share.

Dividends are paid from profit. If a company pays out all of its profits as dividends to shareholders, that may not be the wisest choice in the long term. It would mean a weaker balance sheet and fewer funds to invest in future growth.

The lower the dividend payout ratio, the more sustainable the dividend is, in my opinion.

For example, imagine a business makes $1 of EPS and pays a dividend of 50 cents per share. In the next year, the company could suffer a 10% fall of EPS to 90 cents and still easily fund a sizeable dividend increase to 55 cents per share (a 10% rise).

Based on the Commsec projections for FY25, CBA is projected to have a dividend payout ratio of 78%, and NAB is forecast to have a dividend payout ratio of 70.6%.

NAB shares appear to offer a higher dividend yield, more earnings growth, and a more sustainable dividend, so I would choose them over CBA shares.