If two stock index funds from two different companies hold virtually identical portfolios, doesn’t it make sense to choose the cheaper one? Not necessarily.

In an ongoing industry price war, the giant fund company Fidelity has introduced 0% fees on four stock index funds—the US-focused Fidelity Zero Total Market Index (FZROX)…Zero Large Cap Index (FNILX) and Zero Extended Market Index (FZIPX, small and mid-cap stocks)…and the Fidelity Zero International Index Fund (FZILX). The 0% annual fee undercuts competing index funds, some by nearly half a percentage point. However, the advantage is less impressive against competing exchange-traded funds (ETFs) from other fund companies, which charge as little as 0.03%, meaning that you pay just $3 extra per year for every $10,000 you invest. That’s so minimal that other factors may play a more important role in which fund to choose, including…

You want to simplify your investing life by consolidating all your investments at one financial firm, and that firm is not Fidelity. The “Zero” funds can be bought and sold only at Fidelity.

You have a taxable account. Owning ETFs can be more tax-efficient than owning comparable index mutual funds because many ETFs are less likely to make capital-gains distributions.

In the above cases, your best alternative to the zero-fee Fidelity funds could be ETFs that are slightly more expensive. Two examples that cover the US equity market…

iShares Core S&P Total US Stock Market ETF (ITOT) is available ­commission-free at Ally Invest, E*Trade, Fidelity, Firstrade and Vanguard. Annual expense ratio: 0.03%.

Vanguard Total Stock Market ETF (VTI) is commission-free at E*Trade, ­Firstrade and Vanguard. Annual ­expense ratio: 0.04%.