It's impossible to grasp how the Apple A8 SoC and the Apple S7 SIP compare. There is no worthwhile benchmarking tool on the Apple Watch, so we can't get any Apples to Apples comparison between the two. Apple doesn't specify much regarding the Apple S-series SIPs either, so it becomes pure guesswork. All we really know is that the Apple S6 and S7 are the same chip, and they feature two cores with the same architecture as the efficiency cores of the Apple A13 SoC. This doesn't really tell us much either, as there is no way to benchmark only the efficiency cores on the Apple A13 / iPhone 11 so we have no benchmark on how the efficiency cores of the A13 perform. The S7 only has two of these efficiency cores, while the A13 has four. We have no information on the transistor counts, and we don't really know what the S7 package contains. Does it features a neural engine like the A13 or not? How is the memory controller compared to the A13? We have to remember that the Apple S-series SIPs are designed with ultra-low-level power consumption in mind. It's a different class of CPU compared to the Apple A-series.
I would think the Apple A8 SoC is better performing overall. But pure processing power isn't all that important and meaningful for the HomePod. I think the Apple S7 contains some encoders and capabilities the A8 lacks that make for some significant improvements for Siri due to its ability to do additional hardware acceleration. This is most likely more important than raw computing power for a device such as the HomePod. But with so few specifics on the Apple S7 SIP it's impossible to tell.