The big difference in the European markets versus the US is that there is a wholesale market for subscriptions. In the US the carriers sell direct to retailers whereas in Europe subscriptions are also sold via wholesalers. Given that these wholesalers can buy phones from any manufacturer and themselves subsidize the phone by bundling with a subscription any phone can be brought to market (assuming it has type approval). Some US phones don't even have SIM cards so the US market locks customers far more to their carrier.
So there is more competition in the European market and less control by the carriers of which phones consumers can buy. This means that phone brands are more powerful. That said, some carriers still try to impose their branding in the actual phone (i.e. Orange).
We're still not in the very desirable state of the phone operators being reduced to pure pipes unfortunately.