Certainly some people add lifts and jumppads to their levels for aesthetic reasons and for Z-Axis gameplay. Their differences are great, however, as far as level balancing, continuity and gameplay.
Jumppads are almost always (generalizations are bad) faster than lifts. A player can not easily elude a pursuer since a jumppad simply modifies the players location and has little effect on breaking up continuity of pursuit. There's a slight break in the action as each player modifies their aim.
If not pursuing directly behind the player, hitting a player using a jumppad can be extremely difficult if the player isn't familiar with the level.
Jumppads have greater mobility and flexability that lifts. If you see a person below you when jumped from a jumppad, you can kill him, but when you are on the lift, your line of fire may be blocked by the lift that you are standing on, depending on it's size and shape.
Lifts are generally slower. Even a fast moving lift usually doesn't offer the same throughput as a jumppad. Lifts can, however, be better for escaping from an enemy who is in pursuit. The likliness of successful evasion tends to be a proportional to the lift speed and it's exposure. For example, an elevator shaft style lift protects the player from his pursuer whereas a lift in an open area makes the lift a dangerous commitment.
Special care should be taken with lifts on CTF levels. If a flagcarrier takes a lift and the pursuer can't get on and exit the lift in a reasonable amount of time, the flagcarrier's whereabouts may be unknown if, at the lift exit, there are multiple exits. The defender doesn't know whether or not the flagcarrier went right or left in such a case. In addition, depending on the speed and length of the lift, the flag carrier may end up with a tremendous lead on any persons in pursuit. This can apply to other gametypes as well, but primarily to CTF and Bombing Run.
Of greater danger for exposed lifts is that an attacker knows his target's movement is constrained to the lift and at what speed the lift is moving. This increases the likeliness of the attacker hitting his target, particularly with non-tracefire weapons. This is a good tactic in DM-Serpentine when you defeat Malcolm. When you see the lift go up, and you are in the central area, you can easily lob a flak grenade at him for an easy frag.
A contained lift, however, can offer temporary protection to players within it.
Lastly, lift jumps (hitting jump at the peak of a lift's vertical movement) can allow a player to launch themselves high into the air. This is due to a quirk in the physics code and will not work for Karma-based objects. While the lift goes up the player has great velocity. However, when walking, a player is "stuck" to the floor. This is easily observed in low gravity as your footsteps are not slowed. When the lift stops, the player who is "glued" to it stops suddenly with the lift, instead of being launched off of it as would happen in real life. By jumping at the last second or, even worse, by hammer jumping at the last second, you separate yourself from the lift and are not stopped by it when it stops. Thus you continue with the same upward velocity until gravity pulls you down. On a fast-moving lift, you can really go flying, which can catapult a player into an area they would not normally be able to reach on foot, or allow a player to land directly behind their opponent. It can also be used to make a speedy escape.
Sometimes you might want a lift that follows a curved pattern. This cannot be done using regular movers. However, an ambitious person (other than me ) could fairly easily write a script for a new type of mover that would follow interpolation points. This may or may not work for UT, but for UT2003 it shouldn't be too difficult. Eventually I'll probrably write this class myself, but for the time being I'll just post the idea here and hope someone else writes it.
What hasn't been explored much is the idea of a contained lift where, after a player enters, he takes a slow ride. Perhaps along his route, he'll collect some small health packs. Meanwhile, the attacker can run, dodge forward, or translocate to the lift destination before the player arrives. It might make for interesting choices during the heat of battle, especially in CTF or BR.
The balancing comes in at the speed at which the pursuer arrives at the lifts destination and what obstacles (eg, geometry?, painzones?, no ammo pickups along the way?) he faced.