"Faster" is relative. When comparing modern Linux to modern macOS or Windows 10 on a spinner disk, I can say from personal experience that most Linux distributions are usually faster during general operation.
However, we may start encountering problems to this argument when we're comparing almost 15 year old inherently lighterweight operating systems like Tiger and Leopard to modern Linux distributions, which are held to a completely different performance standard AND built primarily with modern machines in mind (and given that, it's a wonder that Linux on PowerPC performs as well as it does).
In which case, yeah, Linux (or more accurately, the user's choice of desktop environment) might not be faster. But the sheer capability, support, and security compared to 10.4 / 10.5 are what's mainly fueling the drive here.