If you use either of them with async it should be good for the performance point of view as it will not block the resources waiting for the response and you will get good throughput.
HttpClient is preferred over HttpWebRequest due to async methods available out of the box and you would not have to worry about writing begin/end methods.
Basically when you use async call (using either of the class), it will not block the resources waiting for the response and any other request would utilise the resources to make further calls.
Another thing to keep in mind that you should not be using HttpClient in the ‘using’ block to allow reuse of same resources again and again for other web requests.
See following thread for more information
Do HttpClient and HttpClientHandler have to be disposed?