I cannot comment on the decisions of others players I will do my best to respond to the points your brought up.
Since the patch (the akkan colonize and carrier cap buffs) I have based the majority of my strategies around 2 caps for several reasons. The akkan colonize is the best in the game, however it sucks at killing neutrals, the sova is an extremely versatile ship early and mid game and also excels at killing neutrals. But most importantly, I hate the waste from losing your scouts or light frigs to militia whereas the caps are more of an investment that grow from clearing planets. It is a personal preference but I dont think any particular map, opponent, or matchup necessarily favors 2 caps, If i find that most of the stuff around me if light then I typically stick with one cap, but I am usually not that lucky 
And speaking directly in reference to those games, the sova really starts to lose usefulness as the game gets progresses, missile batteries are negligible, their are usually ample counters to fighters, and their is hardly anything worth embargoing. About the only things you get for late game is ionbolt.
I am confused when you say they "throw their caps away", chasing caps through jumps is a skill and sometimes despite your best efforts their is nothing you can do to save your cap. also, its easy to say he failed to get repair bays, but you must consider that they are T2 for advent so the marginal cost of 1 repairbay is pretty high especially at that point in the game, and also his goal was to pressure his opponent not to sit back and allow me to base. Really if he had gotten the repair bays and I never chased his cap with bombers you could for instance say "if he didnt get that repair bays he would have had 5 more ships which would have turned the tide" see how that works? also, if you pay close attention many of the caps I kill is due to ion bolt, its like a frog in a pot of boiling water, so I wouldnt necessarily call it poor play. What would the alternative be? never fight against an akkan unless your sure you will win decisively? if your opponents any good you wont have that option.
"losing" a battle is a pretty subjective matter in this game depending on your objective. I don't consider retreating a loss necessarily, losing a large amount of your fleet however is a different story. Also, Its good practice to not upgrade a contested planet. if you notice the 3 times we battled over that desert I lost only 1 planet upgrade, which was the first one i purchased. After I was forced to base up the volcano all my subsequent attacks were to prevent him from getting a base on my doorstep.
When I had said that "I thought I lost it" or something to that effect, I was talking about my akkan because my repair bays were being drained. I didn't think of drain antimatter at the time, as it is very underused.
In those games the trade was a deciding factor, but it is a 2 sided coin. Tradeports take on average 8-10 minutes to pay for themselves depending on length of tradeline. So if you spend half of all the money you made since the game started on tradeports and you will be essentially 10 minutes behind. Basically by the 10th minute you will be producing the first ship he produced after your first tradeport went up. under those circumstance if you are losing ground during the payback period then you've essentially thrown money away. That game pretty much exemplifies how to hit and run to bide time until your credit income is actually an advantage rather than a liability. for 90% of that game I was outnumbered 4:1. And the fact he deteriorated my credit advantage towards the end just gives creedence to the dichotomy between trade and military. He could have gotten Drone Hosts though, as the only thing I could build that was tough and effective enough to fight his armada were heavies *Shrug*.
BTW, whats your name in game DesConnor?
