The term "site search" means something different to me. That is internal to the site. However, I'm pretty sure that is not your question. So:
SE searches, in general, are pretty quick, display well (even better if you have js off, ads killed, and all scripting disabled---but that is a different story),
Usually provide good results. Bing is better than g ... but that's a personal preference. I am not interested in the under 20 (years) lookie loo presentation and Bing delivers more mature results. DDG comes in second, using their own stuff and what they partner with others. I don't Yandex as I have usually found what I needed with #1 or #2, but I hear good things. Some search engines I avoid for personal reasons. I suspect many have the same expectations, results, and reasons. :)
It all boils down to : "Did you find what you wanted?"
NOTE: Try g with NoScript and Ad Block Plus installed. Makes a difference ... and User Joe and User Sue are picking up on this past, present, and future!