Lossless against lossless
On identical pixels, lossless WebP beats PNG by roughly 26%. Same image, same transparency, same zero quality loss, smaller file. For icons, logos and UI sprites this is free.
Where the gap becomes enormous
Photographs. PNG's lossless compression handles continuous-tone detail badly, so photographic PNGs are often huge. Switching those to lossy WebP — which still keeps the alpha channel — routinely cuts 80% or more.
Where PNG still wins
Compatibility, and only compatibility. PNG has been universal since the late 1990s. Every design tool, document application, email client and upload form takes it without argument, which is not yet true of WebP.
16-bit colour
PNG supports 16 bits per channel; WebP is 8-bit only. This almost never matters for web delivery, but it matters for images heading into heavy colour grading or print, where PNG or TIFF is the right master.
The rule
Ship WebP to browsers. Keep or hand out PNG when the file needs to open in software you do not control, or when you need 16-bit depth.