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I might have to change hosts soon, simply because a competitor is offering a similar service for much, much cheaper. I know my current host cant compete with these prices. We've been with them for several years now.
I understand that you're not asking for this, but here's one more vote against switching from a good host to an more unknown one to save money.
That said, why care what the old host thinks after you're gone? And what makes you think that you can do much about it?
I know my current host cant compete with these prices.
Have you actually asked? Even if they can't match current market prices, they might be a bit put out that they didn't even get the chance to get nearer the mark. If you haven't already, I think you should give them the opportunity (assuming it's purely a commercial price decision to move).
they have access to all our site data, enough said
What do you fear, exactly? Are you hosting "sensitive" data?
If you're a small account, they honestly won't give much of a damn about it. If you're a large account, you may be surprised how they react to the suggestion that they're a little out of touch with market rates and you're considering moving.
Increasing your margin is always something to strive for in business...but you need to find the fine balance between reliability and cost effectiveness. Increasing your volume of sales however is twice as important as your margin. Downtime would certainly not be condusive to volume increase and "customer" satisfaction whoever that may be.
Perhaps you have created a mysql database too, and if you have then you can drop each table to remove it, and then delete the database.
Your stats and logs reside on their server too, but you may not be able to delete them. You should download any of them to own computer if you want them for future reference.