What's the new version like?
I'll say upfront that I never installed version 1.x — why? I was permanently working from home, and whenever I did leave the house there was nobody around anyway. Plus the iOS version apparently wasn't the most polished. So I was eagerly waiting for the version that would use Exposure Notifications introduced in iOS 13.5 — more info here. It took more than two weeks after the announcement before the new version appeared in the App Store.
In the meantime I somehow managed to activate native data collection in iOS (13.7, which requires BT and also Location Services enabled), but I couldn't share it without eRouška 2.x.
I installed eRouška the first chance I got. After a few days I can say it uses only a few percent of battery per day. I keep it off at home and only turn it on when I'm out somewhere with people — on public transport, trains, hospitals, shops, etc.
What about its security? Since the (random) identifiers are generated several times a day and the central server only ever sees those identifiers, it's virtually impossible to trace back your identity. If eRouška notifies you of an exposure, you'd have a very hard time figuring out who it was — you'd have to remember where you were, who with…
Use eRouška — you're protecting others by doing so.