It’s hard to say which one is “better”….
First – there’s the whole underlying “Java vs. .NET” argument – you can’t really compare the frameworks ignoring this.
The whole history of web development in Java with “heavyweight” J2EE apps vs. “lightweight” Spring apps. That in Java there are a ton of web frameworks (MVC and not, open-source vs. Sun-developed) and that Spring MVC had a lot to be based on.
And on the ASP.NET MVC side – the whole history of ASP -> ASP.NET -> ASP.NET MVC. And the lack of widely-used non-Microsoft .NET frameworks – web or otherwise.
Now into the opinionated part…
I’m somewhat the opposite of @Luke101 as I’ve worked mostly with Spring MVC and very little with ASP.NET MVC.
I have to say I prefer MVC-style web development over component-based web development.
I have worked with JSF, which is similar to ASP.NET webforms. (I have to say I liked ASP.NET more than JSF – though this probably has more to do with the maturity of each framework when I used it, and tools available – I used JSF 1.0/1.1 and just Eclipse with no JSF specific support vs. ASP.NET 2.0/.NET 3.5 with Visual Studio 2008.)
As far as MVC frameworks I prefer Spring MVC – but that’s entirely because I’m just more familiar with Java – language-wise and development-wise, as opposed to ASP.NET MVC / C# /.NET. Also, Spring MVC requires Spring, and I like to develop using Spring’s whole IOC pattern and use things already integrated into Spring.
I haven’t tried using Spring.NET and ASP.NET MVC – maybe this would be similar to Spring MVC / Spring / Java.
In the Spring.NET repo there are some examples of integrating Spring.NET into ASP.NET MVC version 3, version 4 and version 5.