I have a website that uses YUI 3.3.0 and YUI 2.9.0 (using YUI 2in3 project), right now I'm trying to improve performance in the initial load time of the site, I followed several tips that I found on the web, but I wonder if I have any improvement if I make an upgrade from YUI 3.3.0 to YUI 3.7.1
What's the difference? YUI 3.3.0 was released in January 2011, and 3.7.1 in September 2012, so that is ~20 months of work by the YUI team and community on the library that is missing (4 versions). Since YUI has hundreds of modules, it's tough to pin-down exactly what changed that could affect your site. It could be very little, or it could be a lot. It's very unlikely that an upgrade could slow-down your site, though. Performance has always been a high priority for the project, so whenever performance wins can be had, they are taken. For example, this recent 3.6.0->3.7.0 introduced some significant custom-event performance improvements (source).
You can take a peek through each release announcement to see if any of your specific needs were addressed:
Also, stop by #yui on Freenode if you have any specific questions about your site and YUI performance.