Question: Can a shared web hosting account be more powerful than a virtual private server?
Answer: No, generally speaking a VPS server with 512 MB to 1 GB of memory and access to 1 core should be more powerful than most basic shared web hosting accounts. In some rare conditions with specific and higher grade shared web hosting accounts. The web host may allow you to use more memory and CPU power. They may also allow you to have more concurrent database connections and php memory script. Unless these rare conditions were to occur a typical web hosting account would be less powerful than a basic VPS server.
Higher tier shared web hosting accounts
If you are using a high grade (very expensive) and highest tier shared web hosting account your web host offers. There is a chance you may have access to a lot of memory and CPU power compared to a typical beginner VPS. The resource limits for concurrent database connections to script memory may also be dramatically higher if you are using the highest shared web hosting account you web host offers. Some web hosts will not allocate a lot of resources to their most expensive shared web hosting account, so for most of the time a beginner VPS would have more power compared to a shared web hosting.
When you are using a typical shared web hosting account. Most shared web hosts will allow your shared web hosting account to access bursts of CPU power and RAM power. These bursts will be short and not permanent. If you were to constantly use a lot of CPU power or RAM power it would cause the hosting environment for other shared web hosting accounts to become unstable. In some conditions depending on how your web host has their system setup. You could end up using a lot more RAM or CPU power than a beginner VPS allocates to you.