While this is a highly debated topic with varying estimates available, the statement that wind turbines kill more birds than oil spills is likely true. Roger J. Lederer, an expert in ornithology who has written many scientific papers and books on the topic claims that over 500,000 birds die due to oil spills yearly. It was difficult to find recent information on turbine-related deaths, but the American Bird Conservatory is a reliable website that analyzes multiple data sources. It is estimated that an average of 681,000 birds die per year (taking into account the increased number of turbines). It is important to note how difficult it is to measure both of these causes. Both of these statistics are likely much higher, though it is impossible to say what the margin of error is.
Sources
https://ornithology.com/birds-and-oil-spills/
https://abcbirds.org/blog21/wind-turbine-mortality/