You have to know bottleneck. At all places only bottlenecks affect performance. In the case of Internet what's the bottleneck? - there is CPU speed, RAM, the ethernet card on your device, speed of your wifi router and then the speed of your Internet connection.
Now, just the CPU speed is not the criteria for a better system. A low CPU speed system may have more cores. Each year many better architectures come which have increased caches and more bandwidth among system components. These are at least as much important as CPU speed. Hence, a newer architecture processor with lower speed may perform far better than an older architecture chip with more speed.