Here ya go, a 1v1 - me(Vasari) vs a hard AI(TEC) on a small random map. I have all settings on fast with large fleets and pirates off. http://dl.dropbox.com/u/6040489/1v1hardAI%28Vasari_vs_TEC%29.record
Notice how I move relatively quickly. In less than 30 seconds I have queued my colony cap ship, 5 light frigates, and sent both my scouts to different plants. I don't build any tech structures until I scout a bit, and when I see a close by ice planet I then put down 2 civilian tech labs so I can research ice colonization by the time I get there so I don't interrupt my colonization.
At 3:30 I colonize my first planet(an asteroid) and immediately build population upgrades and move on to the next planet.
By 6:30 I have my second asteroid and am again moving on right after wards after getting the pop upgrade.
By 15:00, where in your game you had just colonized your first planet, I have 4 planets and have just phase jumped to my 5th. The AI on the other hand has 3 planets about to takes it 4th. Now I got a little lucky here as the AI was stuck behind a desert planet while I had an easier path to early colonization. Had I been in the AI's place things would have been a little slower, but not much.
Also notice how the AI hurts itself early. At 15:00 we're still 3 jumps away from each other, yet it has already researched and built planetary siege frigates. Those things are pretty much useless, especially at that point, and it was a complete waste to get them. Also look at it's research - it's completely haphazard with no real rhyme or reason. There's no reason to have researched an extra cap ship slot, shield/hull increase, weapons damage increase, planetary defenses,
Look how lean my research is compared to the AI's. I've researched 4 things, and salvaging probably wasn't even a good choice, I just like it. The AI has 11 items researched, of which only 2 are even useful at that point, and of those 2 the anti-fighter frigate could probably done without. Ironically, while I have less overall research I have a greater number of labs constructed allowing me to advance in the tech tree to the more important techs faster, especially since the AI wasted it's money on planetary defense to go along with bad research items. You may ask why researching all this is bad - it's since weaponry and defense upgrades are very small % of total health/dps and the others just aren't need at that time. You gain a lot more hit points/dps for the money by just building more frigates rather than making each individual frigate better. It's only the vasari phase missile tech that has any worth in the early game. The others are only useful mid-late game when large fleets are fighting each other.
At around 25:00 I have my first real contact with the AI. We have a small skirmish over a asteroid planet where I have clearly have an advantage(6 frigates vs my 5 with a cap backing me up). Instead of retreating and regrouping with a larger fleet, the AI just fights head on and takes losses that shouldn't have happened. At one point it even sends in more frigates in a small group which have no chance of actually winning. It does retreat those(or whats left) once it becomes obvious it can't win, but it could have saved a good 6-8 ships had it just retreated to begin with. Around 33:30 it jumps in it's whole fleet when it really didn't need to(part of it could have been expanding still) and even jumps in 2 LRF's(long range frigates) early that are, again, a complete waste.
In the meantime I've researched starbase construction in case I need to defend my ateroid planet that acts as a choke point between the AI and me. I do this because, despite being ahead economically, I'm slightly behind militarily. If the AI were to directly attack me I'd be at a disadvantage and probably lose, but since I'm the aggressor at that point, I'm pretty sure that won't happen. Infact, after it does reinforce it's asteroid and I retreat, it sends only 1 cap ship to my planet to attack(more like mildly harass). Instead of throwing down an expensive starbase, I just fight it off with my carrier frigates which I had started building because their a good midgame fleet(I like to go either carrier or cap ships with mass LRF/flak backup), and I micro the carriers around the gravity well a bit to get the most effectiveness out of them.
I stopped playing at around 40:00, but at that point I used my retreating fleet to move to the other side of the sun and start colonizing those planets. I just got the earth planet and will shortly be moving on to the other asteroids. I need to send some scouts in and see where his fleet is at and decide if the starbase is warranted now, but at this point I can do pretty much whatever I want and be fine. I have 6 planets compared to 5, and those 6 will soon becomes at least 8 and as many as 10. I even have a equal/stronger fleet with 254 supply(1 cap, 8 carriers, 6 LRF, 8 LF) vs 234 supply(2 caps, 9 LRF, 8 LF, 1 flak). As long as I don't suicide my fleet I will win.