Airport changes are almost always self connections, which means two separate tickets and no safety net. If the first flight is late, nobody rebooks you, and nobody is holding the second aircraft.
That does not make it a bad idea. It just means the buffer has to be generous and the plan has to be worked out before you fly, not while you are dragging a suitcase through a train station.
What makes these transfers slow
You collect checked baggage, clear immigration if arriving internationally, travel across a city, then check in and clear security again. Any one of those can add half an hour. Traffic and engineering works on rail lines add more.
In large metropolitan areas the airport to airport journey alone often runs between sixty and one hundred and twenty minutes.
Step by step
Step 1: Give yourself a serious buffer
For a same day airport change, four to six hours between landing and the next departure is a sensible target. If the first flight is the last one of the evening, consider staying overnight instead of gambling on it.
Step 2: Choose the transport before travel day
Look at direct coach services, which often exist between paired airports, and at rail routes with a single change. Note the ticket price, the frequency and the last departure. Book in advance if that is cheaper, but keep flexibility if the flight might be late.
Step 3: Plan the luggage
You will be carrying everything. Check the baggage rules of the second airline separately, they will not honour the first ticket's allowance, and a bag that flew free on one carrier can cost a lot on the other.
Step 4: Have a fallback for a late arrival
Know the next departure after yours and roughly what a new ticket costs. Some airlines allow a same day change for a modest fee. Travel insurance with a missed departure clause is genuinely useful for this type of itinerary.
