Magento is resource intensive. We are moving of mod_php setup, and that adds to slowness in some ways. However its puts cap on capability of one user to affect other users easily on same webserver. I've not done this myself, however you can do a local Magento install and move it to server here. Here you can find some hints on how to do this: http://www.magentocommerce.com/wiki/groups/227/moving_magento_to_another_server
It says about ssh access, however it doesn't seems necessary.
On shared hosting, you don't get full CPU and RAM for your website, like your PC. Its not correct comparison. Still, please create a ticket with website and DB info. We will see if this is something we can handle.