Please remember that it is a free service and like with most free stuff you still pay, just not with money. What they earn is your financial information - every transaction you do is logged and used to better target actions toward you.
Ultimately you get convenience and they get an angle to better work you in the future. The stuff you buy, the causes you support, etc., all is recorded and analysed to better understand how to drive you to spend more on shit you don't want in the first place.
I think that moving away from Google wallet is a good decision but getting into the same abusive relationship with another company is not.
In Nordic countries there is MobilePay. I think in Norway they already have NFC payment. NFC payment should be coming to Finland later this year. It's already possible to pay in stores with MobilePay over Bluetooth, but it's a bit of a hassle compared to Google Pay/Apple Pay. MobilePay can be used to pay in online stores that support it, and you can also send and receive money from other people.
Here in Portugal, we have MBWay, works with NFC or QR code, it's free, it also replaces PayPal as you can send money to people and companies with just a phone number. If it could be integrated into an EU system, that would be great.