Comparing Linode's Dual Quad-core Xeon CPUs vs your dual Atom D510 is like comparing a Lamborghini with a mobility scooter.
The Atoms have a tiny percentage of the processing power of modern CPUs. In fact, their performance is even poor compared to CPUs from 6 years ago. They are not built for grunt, but for small low-power devices such as "netbooks".
You will clearly get much, better performance from your VPS.
Now you may be thinking, you have to share the VPS CPU utilisation with dozens of other customers.
Well, even though you may be sharing your server with, say, 31 other customers, doesn't mean that you are getting 1/32 of the processor's cycles. That would only be true if all customers used 100% CPU the whole time, which isn't going to be the case. For most users, CPU usage will come in bursts, and most CPUs remain idle most of the time unless they are doing some sort of ongoing processing.
That said, I have to echo other people's comments that a benchmark like this isn't an indicator of real-world performance, especially because many tasks a server does are IO-bound rather than CPU-bound. So the speed of disk storage (IOPS) matters.
It wouldn't be too surprising given that the CPUs (and therefore the surrounding hardware also) are nowhere near equal. The Atom CPU is tailored towards low utilization, low-power-consumption usage, and lacks a fair number of features in order to reduce its power draw.
Your specs show a number of factors straight away - The VPS has higher clock speed, larger memory bus, MUCH larger cache.