Personally I would forget about performance in this instance and focus on what the image is:
1) Image = content
2) Background Image = design
The way I tend to think about this is, do I want the image to appear on all screen sizes, on all devices, with CSS turned either on or off? Do I want the image to be “indexed” by Google and Facebook. If the answer is yes to all or any of these questions, then usually the image is “content” and you should use an IMG tag.
If you want a different image to display at different screen sizes (or no image at all on certain devices), or if you’re happy for the image to not appear on a print out, or you’re happy for the image to not appear if CSS is turned off, then usually the image is “design” and you should use a background image.