For compatibility sake, I'd recommend the full absolute URL (second URL) in your case. I'm not sure how many browsers support protocol-less URLs but I bet some older browsers like netscape won't understand protocol-less URLs.
If you're trying to save the number of bytes on a page used for linking to external resources, then have your resources stem from the same folder, then add the following between the
</head> of your HTML:
The value for href is the base folder where all your resources are stored plus a trailing slash.
Then if all assets are in the exact same folder, you can easily call them by filename such as:
<img src="somefile.jpg" width=100 height=200 alt="a picture">
If all the above HTML is used unmodified in the same webpage, then the image requested will be:
This is because the base tag sets the default folder for the resources on the page.