What each one is
A burner phone is a cheap handset with a prepaid SIM you use instead of your main one. A virtual number is a number with no physical SIM at all: it receives SMS and calls in a dashboard you open in a browser.
For online sign-ups, virtual wins
Most privacy needs today are online: verifying an account, selling on a marketplace, joining a service you may not keep. A virtual number handles those without a second device to buy, carry, and charge. The code lands in your dashboard in seconds.
Where a burner still fits
If you need to make and take calls on the move in a place with no data, a physical handset has its place. For most people, that need is rare, and it comes with the cost and hassle of a second phone.
Privacy of the purchase
A burner still involves buying a handset and a SIM, often with a card, and some countries register prepaid SIMs to a person. A virtual number bought with crypto has no card and no ID to buy, so the purchase is not tied to you.