There are lots of different online performance tests:
Also there are several desktop/client software such as:
I just want to decide if my hosting provider has a good enough performance or if I need to switch my hosting to another provider.
So, which tool should I use to compare my hosting provider with other hosting providers?
It depends what are you looking for: loading speed it's just an effect of network speed (which often is what you are looking for) and server side processing performance (hardware performance).
One factor to keep in mind is where the host is located: if your audience it's mostly in Europe, would be useful to get an host close to the main European backbone. Similarly for other Geographical locations.
After you have decided this, you could use stress-test tools like siege (on UNIX) to create lots of requests to a webpage and see how the host behaves under stress (using the tools you mentioned).
In the case of shared hosting and virtual server you can never be 100% sure that an host is going to be consistently fast (or slow), as your test might be influenced on other site's activity on the same host. It would be good to test during different times and for a relatively long period of time (for example one test every few hours for a week), in order to have a good "rough idea" of the host's speed.
To be fair, you should test the exact same site(s) and page(s) on every host (with the same frequency).
as other have already pointed out, 'speed' can mean many thing. in those cases i suggest a so-called 'stresstest', that is pushing the server to its limits to see ho many pages it can serve when many browsers are connected and different pages are requested at the same tima. I normally use Jakarta Jmeter finding it a really effective tool
You may also want to check out this free tool http://www.bitcatcha.com/ where it measures the response time of the server. The tool will ping the server from 8 different locations around the world to simulate actual browser request in different part of the world. The response speed will be recorded and then the results will be benchmarked against the Top 10,000 websites’ server response time on the Web (Alexa Global Site). You will get to know where does your server stand against the top guys.
FYI, Google's webmaster-recommendations is to have a server that responds at 200ms or quicker.
Disclaimer: I co-develop the Bitcatcha server speed checker.