Firstly, note that:
Case 1: QR Code has no design, standard design, or custom with logo
In this case, you can export the QR Code image in both raster (PNG, JPG) and vector image formats (EPS, PS, SVG, PDF).
If the target destination of the QR Code is web (email, website, mobile app, etc.), then you can export the QR Code in raster format i.e. PNG or JPG. Note that raster can also work with small-size print jobs such as business cards.
If the target destination is print (especially prints larger than A4), then export the image in vector format (EPS, PS, SVG, and PDF). Popular image editors such as Adobe Illustrator, Photoshop, Corel Draw, and Sketch (Mac) can import these vector image formats.
The size of the vector image can be increased or decreased infinitely without compromising on resolution.
Case 2: QR Code has custom background design
In this case, you can export the image with QR Code in raster format only (PNG, JPG). The image size will be the size of the image imported.