The train is going to be cheaper than the plane, except that there's a new airline GermanWings in Germany that sometimes is a tad cheaper. There are always deals too, like someone else said, so talk to an agent before buying.
The train through the Alps is spectacular. I take it every July from Munich to Zagreb.
I don't see any reason to buy a Eurail pass if you're only going to be there 9 days.
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