Ah, this is one graphic design question we get asked all the time. What is the difference between the two?
Put simply, a vector file (like an .eps or an Illustrator .ai file) can be blown up to whatever size you like, without losing resolution.
A JPEG is what’s known as a bitmap file. It loses resolution as you enlarge it. Photographs are usually JPEGs which is why, if you use one at a size it can’t cope with, you get pixels like half bricks.
Most logos are designed as vectors, so they can go teeny tiny or multi-massive without losing any definition, giving good brand in the process.
We sometimes have to redraw clients’ logos from bitmap into vector so they can be more versatile, but if you’re starting your logo from scratch – go vector. There’s nothing so disheartening as seeing your lovely logo lose its crispness when it’s blown up.