It depends how you are getting there... If you are using Vertical Speed, then the version implemented in the (pretty abysmal) default airliner autopilot is plain wrong and you shouldn't be using it. In a more realistic sim such as the PMDG B744, the two vertical path modes that will get the aircraft to move to and stop at a pre-set altitude are FLCH (Flight Level CHange) which is usually over by the speed controller, which causes the aircraft to climb or descend at the speed you set in the window or VNAV (Vertical NAVigation), which will cause the aircraft to change altitude depending on the settings in the FMS.
If you are flying manually, not following a flightplan, then FLCH is the way to go. If you have fully filled in a flight plan with cruise altitudes, speed restrictions et cetera, then the fully managed VNAV is the best option - although most real world flights will simply be "take off, press LNAV, press VNAV, turn on autopilot, sit back and monitor" in theory. It doesn't always work that way due to ATC vectors, weather, traffic and suchlike.
Edit: It's also worth remembering that you do have to change the altitude set on the glareshield panel for step climbs and any form of descent. You might, I'm not 100% sure, have to press the altitude setting knob on the B747-400 to tell the system to accept your change of altitude. But I might be getting confused with Airbus there!