ICE, duration 5:40. Cost around 100€ With Bahncard 50: 76 €
Same with slow train: duration 11:00, cheapest ticket 29€
Flight around 200 Euros, Lufthansa 300+€, Flighttime 1:15, Travel time: around 3.5 hours.
Hamburg -> Frankfurt. 400km
IC, duration 3:30, Cost starting at around 75€, with Bahncard 50: 53€
Business Trips: company pays. Many business trips in one year: get a Bahncard 100. Company pays. Costs 4400€. Unlimited travel with full flexibility within Germany. For example one trip Hamburg<->Frankfurt per week and the Bahncard 100 is easily more convenient.