Hi,
I've had customers before who made the same discovery and were quite startled, and I've helped them through the process of optimisation of their VPS to sort this out.
I have 15+ years of Linux admin, and plenty of experience of both of the 'off the shelf' web apps you mention so I'm pretty sure I can sort this out for you.
However, as sometimes happens, it may be that the VPS infrastructure at your new service provider is just so fundamentally flawed that it's unfixable by anyone but them. That is fairly unlikely, and if the situation resolves down to that I'll give you clear evidence as to why so you can get your service provider to fix it, or move to another one.
Some customer testimonials for reference:
"Thank you, you're a God-send".
Josh Strike - Strike Sapphire
"Thank god for you being available, dont know what we would do if you were not around."
Matt Norris, Strand International / Easy Play Poker
Yours,
Kev Green,
oRe Net.