As someone who has hired front-end developers recently, I would recommend that you choose the sites that you originally have from design school, but only show the ones that you believe the company interviewing may like to see. While it is impossible to know, you can generally, read about the company on their site, blogs, press-releases or by talking with people that do/have worked for them.
By learning about a company you are showing initiative beyond your design capabilities. This can be a nice influencing mechanism.
If while working on the bits of code that you have strewn throughout the big-companies' website, you have scripted any more modern web work like media query usage, jQuery (keep on plugging away on this, many employers know about it), and emerging CSS 3, and dare I say HTML 5 - even if you don't agree with HTML 5 it is helpful to demonstrate knowledge to defend your position.
Show some modern stuff your doing. Yes it is more work and you may be tired of doing it once you get home, but by advancing ideas and designs that you can not realize at your production orient work, can demonstrate your skill, and that you stay current. This is important to those hiring you.
Finally you can speak about how you have also fit into a larger team to do production level scripting so it does not always 'have to be about' doing full sites for you. I know if I was hiring you, I would see this. Give some examples of some of the more interesting/innovative pieces you have done at the larger company.
Doing these things will show potential companies that you court that you 'go the extra mile', care about what you do, a team player, have knowledge, and are a hard-worker; all things that employers are starved to see.
I can tell you when I hire developers, it sometimes takes 100 or more interviews before I find someone with these qualities and I snap them up faster than I can type (which by the way is only medium fast )