It sounds like you're building a large army and using it to gain map control, but then are falling prey to things like drops and backdooring.
If you have map control your first thought should never be: Crush my opponent, as you're essentially sacrificing an advantage (map control) for an unsure victory (because he doesn't control the map doesn't mean he can't take you). Instead your thought should be: take the map. I think you'll find this change in philosophy will lead to situations where you have a much more powerful economy than him and you're able to kill him with attrition.
Now if you're falling prey to things like BD here is a quick check list for you:
- Are you scouting? an Observer should be the first thing you build out of Robo. If you don't go Robo, a Hallucination works just as well. Sometimes scouting means sacrificing some Zealots in a pointless charge to just get inside his base.
- If you're scouting, are you seeing it coming? Overlords on the edge of your base, Starport with Reactor + 3 Rax, all of these are indicative of certain strategies you should watch out for.
- If you see it coming, how are you responding? If you have map control that means you should be able to respond quickly. Shutting down these back door attempts is often a bigger victory than a straight up conflict
- Finally, Do you have map control? If you don't have map control that means he does, and if he's beating you with map control then your problem is not "how do I deal with a base trade?" but rather, how do I regain the advantage.
I'm a protoss player so I'm on the opposite end of your situation.
I believe the way for Terran to win is to never directly encountering the army.
Use drops to keep his army out of position and win the attrition war. What I mean by this is that when they pull their army back to base, use your main force to knock out expansions. If you can keep denying expansions, they can't replenish their force as quickly as you can, or they can't afford it. If they don't pull their army back, they're warping in units at home, which means their front line army is that much weaker.
Maurader/ghost/viking is a decent composition, but you have to have marines in there as well. Stimmed marines are the highest DPS unit in the game (not counting storms/fungal over a group of units). When the fights start, make sure your vikings are target firing the colossi, a few shift right clicks in the fight will reduce their numbers much better than just A-moving them in. By keeping colossi numbers down, your infantry army is that much stronger.
Your ground force should be something like 60% marines, 35% mauraders, and a few ghosts. That said, your army composition should be reflective of what he's making more of (This is assuming an infantry force). If he has more zealots get more marines, more stalkers? More mauraders. I also assume that you're making medivacs to help your healing.
You also mention that it's the norm to get +3 armor really fast, and it's right, I do as well, marines do 5 damage (no upgrades) zealots have 2 armor, take off 2 more from guardian shield and you're tickling the zealots with no upgrades. Upgrades make them that much stronger. The answer? Keep up on your attack upgrades too. They essentially cancel out if you are just as high with your attack upgrades. And since you need to make the armory to keep upgrading, might as well do air attack as well (so your vikings can knock down colossi faster).
It's also key to keep their colossi numbers down. Losing 2-3 vikings to take out 1 colossi is huge and well worth the trade. This can be combined with drop play. If you see that they are back at base dealing with your drop with warp-ins and haven't moved their army, stim in and attack his main force before he reacts, by targetting the colossi and taking them out of the battle, your infantry force will be that much stronger.
Best Answer
Line of sight is your ally on this map. There is a elevated area to the northwest of your base with a few ramps leading up to it, try to place your bunkers/tanks at that ramp rather than in your base, also put up a few turrets to prevent annoying science vessels.
As for the northeast entrance, send out a engineering bay or barracks out that way to scout to extend the LOS for your tanks guarding that entrance. If your tanks get off the first shot, you will beat them. With enough tanks, they won't even be able to finish seige mode before dying.