Hi Sam,
the great thing about Serilog – and really the thrust of this article – is that it allows structured logging. You can embed your variables into the log message, which then become searchable. You can also add context which gets automatically added to every logged message.
ELMAH tends to be primarily used for catching and logging exceptions, but by adding a global exception handler, Serilog can do this too.

Some people use both, but I would stick with Serilog, it is definitely worth getting to know.

Thanks for your comment,

Darren