It's not a real problem. If it were actually a problem you should be able to walk under a wind turbine and find a bunch of dead birds/bats. The reality is you might find 1 or 2, but not enough to actually observe any sort of impact on the population. Outdoor cats are a far bigger menace to birds and bats.
So yeah, you build a ton of those turbines. Because by the time you can deploy 1 1GW plant (10 to 20 years) you can install 10 or 20 times that much power generation via wind. By the time the nuclear plant is operational, you can be talking about refurbishing some of the early installed turbines.
A nuclear plant requires fuel sourcing, waste management, engineering and planning, constant management and monitoring, security, and a fairly large construction footprint for the likes of the cooling towers.
Wind requires someone to go grease the gears once a year.