The HTTPRequest is "kind of" a wrapper for curl. This two quotes from the manual should give you a clue:
It provides powerful request functionality, if built with CURL support. Parallel requests are available for PHP 5 and greater.
The extension must be built with » libcurl support to enable request functionality (--with-http-curl-requests). A library version equal or greater to v7.12.3 is required.
Said that (and said that I've never used this extension myself), looks like if you want your code to look more object oriented, you can go for this one, but it might be a bit slower, though nothing compared with the external call that you are going to make, so I won't consider performance to make my choice. I would give preference to the fact that curl is built in and this other you have to add it yourself, which is unconvenient and reduces portability in case you want to host your app in a shared environment that you don't control.
For the needs that you explained in your question, I would definitely go for curl.