Edit: and by this I don't mean that one of us is wrong. I mean that it might depend more on the application and its memory allocation patterns than the runtime.
The main thing is dotnet had this figured out 10 years ago while Java is still struggling.
.NET, by putting all their efforts into just one GC, has absolutely reaped a lot of benefits in terms of working well without any fuss. .NET also has better ergonomics around memory management. For example, it has much clearer and stronger guarantees about what state the runtime environment will be in after an out-of-memory error. On the other hand, I'm sure that making these guarantees have at times constrained the things that .NET can do with its garbage collector.
Java, by making the GC a plugin, has certainly spread its efforts thinner. It's also turned the Java-facing side of the memory management subsystem into a somewhat scary and mysterious black box, since that very swappability means that the application itself can assume almost nothing about its behavior. On the other hand, if ops wants to put the effort into tuning it, Java lets them have a lot more ability to control an application's memory and performance characteristics in production. It also leaves a lot more room for boutique JVMs with their own special memory managers.
Which approach to prefer is, I think, as much a matter of personal or organizational values as it is about technical merit.