The Aile Strike is badly outclassed by the ZAKU Warrior. The only advantage it might have is in mobility as long as the fight occurs on Earth, and a very slight advantage in close-quarters combat due to its beam saber having a longer reach than the beam tomahawk.
The ZAKU Warrior has a significant advantage in endurance because, being newer, it will have a more efficient powerplant/battery. Even if we assume both machines have the same battery capacity, the ZAKU still has an edge for two reasons:
1. The Strike's Phase-Shift Armor is constantly draining its battery, with a significant increase in energy expended whenever it has to defend against, for example, an explosive like the ZAKU's grenades. The ZAKU, which lacks Phase-Shift, does not have to worry about this.
2. The ZAKU's beam rifle does not draw power from the suit's battery, unlike the Strike's. Instead, it uses its own separate energy drums, of which it carries a possible total of three - one already on the rifle, plus two mounted to the underside of its shield.
So what's going to happen is that the ZAKU will move to keep the Strike out of close-quarters striking range and attack with its beam rifle. And before too long, the Strike's power will run out. Once it does, it's basically a sitting duck.
On Earth, the Strike has a much better chance at evading the ZAKU's attacks, so it might be able to barely eke out a win if it can use that advantage to move into close range in spite of the ZAKU's efforts. Meaning I'd put its odds at 50/50 at best.
But in space, that advantage is significantly lessened, so the odds of the Strike winning decrease substantially.
Overall, I'd give it to the ZAKU eight times out of ten.