Here's a test. Seems strpos() and strstr() are very close. Really, the main thing that is different between them is their return value (false). And even that will be the same if the needle is not found in the haystack.
However, stristr takes 3 to 4 times as long to complete. If you don't need to do a case insensitive match, then even if the time is in milliseconds, and "inconsequential," a good programmer will still use the faster function. Always make your code as scalable as feasible. I think it's fairly feasible to omit an "i" from your function, don't you? Especially if you are searching for a symbol like ? and =.
My server is hosted, which means there are other sites on the same server. To truly test this purely, it should be done on a server with no load on it. If you want to do so, here is the code.