Copying site from external LAMP VPS to Debian/Nginx Linode?

I don't believe that nginx (or any other web server with one exception) supports .htaccess files, which makes perfect sense; .htaccess files are just local Apache config files. They aren't needed with most other web servers. For example. lighttpd provides various matching mechanisms to allow such things to be placed in the main lighttpd config file.

As for that exception that I mentioned, the commercial Litespeed server supports Apache's config file and .htaccess files, as it's designed to be a drop-in replacement. The free version has limitations, however.

For some reason I thought nginx did, which is why I selected it over Lighttp.

The problem I have with .htaccess is they handle some url rewriting, and as the links are all known know I want to keep the links the same.

Is nginx of lighttpd easier to get to work with the data in the htaccess files?

You know, Apache will read your .htaccess files without you having to do any work at all.

True, but I was lead to believe by someone who knows more than me that because I was hosting video, I was better off with lighttpd (which YouTube uses) because it'll be faster.

If this isn't the case I may as well just stick with a LAMP stack.

You would be better off, although apache can be tweaked to be a lot more efficient than the default config (which is just plain bad).

nginx/lighttpd both support URL rewriting, they just don't do it from .htaccess files. In lighttpd's case, it does it from the main config file.