One of the problems I have with Apple Watch series 1 is the connection speed. Sometimes it takes a while for the weather, events near me or apple map to appear. I assume this is because of the wireless connection speed. My iPhone can load these data almost instantly when sharing the same wifi network. I wouldn't mind upgrading my Apple Watch series 1 to 3 if the wireless speed is much faster.
In terms of specification, the Apple Watch series 1 and 3 support the same wireless networking protocols (80.2.11 b/g/n on 2.4 Ghz) and their associated theoretical maximum speeds.
However, effective wireless networking speed is affected by many other factors than the wireless protocol used - for example the interface speed between the wireless module and the main CPU, and the processing power of the CPU itself.
In reality, I don't think your problems with slowness in weather data, event data, etc. coming in is really related to wireless networking speed. It makes more sense that they are slow because the main CPU is busy doing other stuff, and background tasks such as retrieving weather information is intentionally underprioritized.
So in practice I would expect an Apple Watch 3 to perform these tasks much faster than the Apple Watch 1 - simply because the Apple Watch 3 has a much faster CPU and is in general a much speedier watch.