We recently did some quick tests on the results of some projects that we just finished migrating to compare the binary size and memory footprint of the resulting migrated .NET application and the original Visual Basic 6.0 application. Here is a brief summary of the results.
Binary Size
We have seen that binary sizes remain very similar or decrease by a small margin when compared to the original Visual Basic 6.0 binaries. There is a small amount of application re-factoring that contributes to this reduction, though, such as consolidating all shared files to a common library (instead of including the same files in several VB6 projects, which increases the code base and binary size).
You do have to take into account the space required by the .NET Framework itself, that varies from 280MB to 610MB.
Memory Footprint
Our observations on the memory footprint of migrated .NET applications, when compared to the original VB6 applications, is consistent to what we've seen with the binaries' size. .NET applications have higher initial memory consumption, since the .NET Framework sets up the stack and heap space at startup, and you have to add the memory required by the JIT compiler. Even with these constraints, a quick revision of applications that we've migrated for customers shows that the memory consumption is, on average, around 10% less than in VB6 (these are no scientific measurements, just based on monitoring memory consumption during the execution of test cases).
We have also seen that .NET normally maintains a more consistent memory usage pattern, while VB6 applications has more peaks where the memory consumption goes up, then back down. This is caused by the .NET Framework holding on to resources until the Garbage Collector runs, and the overall improvements in memory management included in the .NET Framework.
.NET applications have a memory overhead associated with the .NET Framework itself. This is more noticeable in small applications, but overall, is a tradeoff required for running on a managed environment. According to the .NET System Requirements, the Framework requires at least 96MB (256MB recommended) of RAM to run. In our experience, however, you should have at least 512MB (1GB recommended) of RAM to run migrated applications comfortably (on Windows XP).