I'll preface this by saying I haven't ever done work on the Microsoft stack, so take this with a grain of salt.
Community support: Java tends to have a more active community (and much more diverse universe of new open source projects) than .Net (related to below).
Difficulty level: I'd say the Java/Spring stack is more difficult because Java developers tend to use more community projects and have to know which ones to choose in which circumstances (e.g. what logging framework to use? What database connection pooling library to use? What testing framework to use). That being said, most decisions you have to make have choices that are vastly more popular than others. My impression is that .NET guys use stuff from the standard library almost exclusively. If it's not provided there, it's a problem they never thought to solve or maybe write their own (usually the former).
Career prospects: I'll get hate for this probably, but Java/Spring has more jobs than .Net. .NET Core even more so because it's new. Most .NET jobs out there are going to be not Core, and not on anything other than Windows. LinkedIn search for jobs in United States shows 97,103 for Java and 36,448 for C#. That's not to say some individual city might not have more .NET than Java, but by and large Java is bigger. Also, .NET is not dying at the same pace as say Ruby on Rails (sorry Rails fans). I'd say it's ticking very slowly lower, maybe even holding steady. I wouldn't say you're screwed career-wise if you choose .NET. C# is also pretty similar to Java from what I've seen, and I know professionals that have transitioned to Java (though interestingly, I don't know any that did the reverse). Several companies have basically no .NET footprint, for example, Amazon, Google, Facebook, LinkedIn, Twitter all have Java, but basically no C#.
Specialized fields: Neither Spring or .Net are going to be a thing in a field like data science. That's exclusively Python (some R) for the most part. The only exception being that there is some Java in Hadoop, and Scala in Spark (which runs on the JVM). But I think those are generally more for data products being created, and not data science work. I'm also under the impression this is increasingly less the case than historically. Some other specialties might make Java useful, for example Android development.
In short, Java is the COBOL of the modern enterprise (which is both a good and bad thing). I recommend it to anyone over .NET, but not for technical reasons. It's for reasons related to the questions you asked. There are actually reasons I think CLR and C# are actually better from a technical perspective than Java (unsurprisingly, since they had the benefit of hindsight). But that's not what you were asking about...