This could have a multitude of reasons, for your observations, but none include the specific technology that is redirecting the traffic. That in this case proxy appears faster is just a coincidence, and the question title is extremely misleading. I suggest to change the title into something that doesn't assume it's precisely proxy is constantly faster than VPN, because it is not. Something like "why different paths show different bandwidths" will be more appropriate.
What you observe is that certain path for the traffic is better that other. Why is that? Well, it could be routed through wider link; ISPs can apply selective shaping with different thresholds towards different destinations, and so on. Some ISPs can also detect and downregulate VPNs.
VPN providers also can place artificial limitations or simply have limited bandwidth for each connection leg. Consider a VPN service to be a farm of many servers with multicore processors such a that each core only can handle 100 Mbps, but since they balance different connections to different cores and servers, they can achieve a practically unlimited aggregate service bandwidth.
The general reason is that traffic is almost never forwarded towards "fastest possible" link, but usually "cheapest possible", and that the join of several "cheapest possible" links is unlikely to be the best if you consider Internet and try to find the widest pipe between point A and point B. Sometimes, you can build the better path by hand using VPNs, proxies and so on, and if it's found, it doesn't matter which technology you use, all of them will show approximately same bandwidth.
There is one special condition that can make the proxy to show better bandwidths, and that is the case of high latency link when the proxy system divides the latency into approximately equal parts. It is connected to the TCP throughput specifics. With maximum TCP window size 65536 (bytes) and round trip time 1 sec, the maximum throughput of the single connection will be 65536 bytes/sec, but if you place a proxy server in the middle and have its RTT to each leg 0.5 sec, each TCP leg will have throughput twice as fast and so will be the whole perceived bandwidth on average. VPN in place of the proxy will not reduce end-to-end RTT and the bandwidth will not be doubled.
However, to increase the bandwidth tenfold this way you'll need to chain 9 carefully placed proxies, so this is very unlikely to be the reason in your particular case.