Scenario

I don't think anyone has ever built a list to win on scenario, I think it's always an attrition list that can also dominate on scenario and you simply take the opportunity to win on scenario if it is presented to you (if you go first on a scenario you can gain a significant advantage on). I think one of the main reasons you don't see pure scenario lists the same way you see pure assassination lists is that it makes a huge difference whether you go second or first and which scenario it is.

List Building
While no one builds lists purely for scenario you often want your attrition lists to contain the pieces you need to win via scenario. You can do that with assassination lists as well, it make a very good bluff and can force your opponent to put their army somewhere predictable so you can line up the assassination. The main things you want to enable yourself to play for scenario are:

fast, low point solos - the best models in the game to control flags or contest zones, particularly if they have a ranged attack they can use while doing that. You don't want to have to keep a whole unit within 4" of a flag or objective, you want that unit to be fighting or at least blocking your opponent so they can't contest. Same with a heavy. You want something cheap controlling your flagjective so that you are taking as little of your army out of the game as possible.

Models that can move enemy models - Repulsion is awesome for scenario. So is bulldoze. Gun mages, druids, Battle mages, there are a lot of models that can move other models around. This includes casters with spells that allow you to move enemy models. Rampager, Telekinesis, Hellmouth, Force Hammer, Thunderstrike, Gallows. They can use these to move key models out of the scoring zone.

Models that cannot be moved/are difficult to kill - preferably both but a devastator in the middle of a 12" circle needs a lot of movement to be pulled out of the zone and the ARM 25 makes it very hard to destroy. Colossals are ideal for this as they are the hardest models to kill in the game and they cannot be moved. They also can often contest both scoring zones. The other models that are really good for this are incorporeal solos, and models like Reinholdt who is DEF 16. Reclaimers can often do it too (auto 1 damage point to anything that comes in melee range).

Casters with SPD debuffs
This is the big one. If you go first, rush up and the feat turn 2 you can put a lot of armies in the position where they can't possibly contest zones on your turn. It also works to a lesser extent for casters that make you take damage if you move up (beast/jack heavy armies will mostly ignore it but works fantastically on infantry). You can get a point, push forward again so they have to fight through most of your army to get to the zone and then kill anything that does. Against an inexperienced opponent you can do this going second as well as often they don't think to rush the zone and instead hang back a bit to protect their army.

Casters to watch out for: Both Deneghras, Grim Angus, Haley2, Krueger2, Irusk2 (technically, never seen it but that might be because he doesn't have iron flesh), Magnus2.
Damaging casters: Old Witch, Harbinger
Other casters that can cause scenario issues - Bartolo Montador, Gorten (have to be really close but as his feat pushes stuff as well as SPD debuffs it has an excellent scenario effect), MacBain (feat on boomhoowlers blocking off a scenario zone).

Playing for scenario
The first thing to do is to identify early on whether you are going to be able to win via scenario. If not play attrition. Whenever you are playing scenario you will find yourself sacrificing models for points, it puts you way down on attrition. If you aren't going to be able to win that way you are going to lose the game trying. This depends on a lot of things, firstly the scenario being played - how easy is it to score? how easy will it be for your opponent to contest the zone? It depends on what you are playing against. If your opponent has a colossal and you are relying on pushes to score then don't play scenario, go for attrition.

If you have determined that you can win by scenario then pay attention to the scenario conditions, focus on preventing your opponent from scoring not on killing models or not dying. You will often have to give away a whole unit to your opponent, run them out in front of the zone to make it harder for your opponent to get through. The pieces you need to protect are those that can win the scenario for you, everything else can be sacrificed and you need to not be afraid of losing half your army without doing any damage as long as it is going to put you in a position to win the scenario.

Playing Against a Scenario Caster
Run at them. You need to get across the table, you need to have models in the zone turn 1, especially if you go second. You need to have as many models as possible too as they will be able to kill some models as well and feat to keep you out. Don't be afraid to lose models just to contest the scenario preferably fast low point solos. The most important thing is to never give up a point in your turn. You may have to give up a point in your opponents turn, that's OK as long as you are in a position where you can fight back and make that the last point they score. Remember that you can trample warjacks/beasts.

Try to take out or at least neutralise their scenario pieces. Gun Mages will not do anything if you run and engage them. Put a colossal in the zone and protect it. If all else fails camp all your focus and toe your caster into the zone. The Harbinger may be one of the squishiest casters in the game but if she camps 11 focus she's ARM 25.