Same company with different prices, no broker commission with Connect. ZH just put up my premium mid contract, ZH connect was cheaper than my original premium & for the first time in 17 years everything is in English.
Just as in other countries, rates will vary depending on circumstances. We changed one of our cars earlier this year (from Pug 206cc to Audi TT) and were not totally surprised that the premium went up significantly with the existing insurer (ZH). What was a surprise was that a quote from Axa, for identical cover, was something like 40% cheaper (~1400 compared with 2200). On the other car I've stuck with ZH for the moment, as they're about the same price, so it's clearly something to do with the specific model.
As for Zurich vs Zurich connect, I've always found them to be identical. IIRC we had one policy with each, just by chance. Every time I've done comparisons they've come out just the same.