Changing airports is almost never something you planned. Düsseldorf Airport to Hamburg Airport is 398 km and about 4h 06, and a car covers it in one leg with no change and no ticket barrier between you and your suitcase.
The pickup is driven by your inbound flight number: the driver watches the actual landing time and waits 60 minutes free after touchdown, which is what a diverted or delayed arrival needs. At the far end the drop-off is at the correct terminal for your departure — Hamburg Airport has 2 and the wrong one costs a shuttle ride you do not have time for. Tell us the departing flight at booking and the schedule is worked backwards from its check-in deadline rather than forwards from a convenient departure. We run the same journey to Stuttgart Airport, priced the same way.
Luggage stays in the car for the whole 4h 06, which is the single biggest practical difference from any rail route: nothing is lifted onto a train at Düsseldorf Airport, off it again at the interchange, or onto a second one for the run into Hamburg Airport. If the airline has rebooked you and is reimbursing ground transport, the invoice shows the route, the date and the fare in a form an airline will accept.
Checked bags are the whole argument
With cabin baggage only, the rail route between two airports is an inconvenience. With checked bags it is a different journey altogether: every interchange means lifting cases onto a train, off it, up a staircase when the lift is out, and along a platform to the right carriage. A car takes the bags once at Düsseldorf Airport and gives them back at Hamburg Airport. A saloon holds three large cases, a van takes seven passengers with luggage to match, and if you are travelling with sports equipment or instruments — the things that make a rail change genuinely hard — say so at booking and the right vehicle is sent.