Or, lets pick something the OP asked about - Munich to Luzern.
If you take the train, the closest airport to Luzern is Zürich, so either way you go by train from Zürich HB to Luzern. The difference is Munich Hbf to Zürich HB.
If you go by train, the fastest connection and lowest fare is the EC. Time from Munich Hbf to Zürich HB is 4H33. Cost with an advance purchase Saver Fare is 38€ for two.
If you fly, the S-Bahn to the airport leaves from the Hbf and takes about 40 min and costs 22 euro for two people. Figure 10 minutes to get from the S-Bahn station to Terminal 2, and 90 minutes preflight time. Only Lufthansa and SwissAir fly direct to Zürich in 55 min for 717 euro for two people. Figure another 20 min to get to the S-Bahn at ZRH and 12 min and 6,30€ from there to Zürich HB.
So flying might save you 45 min at an additional cost of over 700€.
But let me pick a couple of places I know a little about. In 2012 I went from Zwiesel, in the Bavarian Forest (you see some of us don't just visit big cities) to Prague. The trip by train took 4h41 and cost me the equivalent of 11€ in Czech Koruna.
The nearest major airport to Zwiesel is Nürenberg. Zwiesel to Nürnberg takes 2h50 and cost 28€ with a Bayern Ticket. The lowest fares I find are 1190€ for two for the 1h55, one stop flight to Prague, so already you've spent more time and a lot more money flying and you haven't gotten to downtown Prague.