It isn't that there are 'better ways'...just different.
The use of <blockquote> is more
semantically correct when creating a
block quote, whereas a <div> is a simple division, and classed paragraphs are just formatting the paragraph. Yes, you can make them look the same, but using a blockquote when you have a long quote (usually of multiple paragraphs) sets up your document properly.
P.S. You can style blockquotes to look any way you want with CSS and the target renderer will treat it just as well/badly as it would treat any other CSS.
example: