A friend of mine said that using <div style=""></div> instead of compressed css file put as link href at the head section gives some performance boost. Is that true?
The performance boost that your friend mentioned is probably too trivial compared to the amount of performance boost (through other factors) using a CSS file.
Using the style attribute, the browser only paints the rule for that particular element, which in this case is the <div> element. This reduces the amount of look up time for the CSS engine to find which elements match the CSS selector (e.g. a.hover or #someContainer li).
However, putting styling at element level would mean that you cannot cache the CSS style rules separately. Usually putting styles in CSS files would allow the caching to be done, thus reducing the amount of load from the server each time you load a page.
Putting style rules at the element level will also make you lose track of what elements are styled what way. It might also backfire the performance boost of painting a particular element where you can repaint multiple elements together. Using CSS files separates the CSS from HTML, and thus allows you to make sure that your styles are correct and it's easier to modify later on.
Therefore if you look at the comparison, you would see that using a CSS file has much more benefit than styling at element level.
Not to forget when you have an external CSS stylesheet file, your browser can cache the file which increases your application efficiency!