I think an aspect of Zho combat capability one must count is cohesion.
They'll stick together and follow orders to the death.
That is a weakness too, if the leadership is not technically/tactically competent.
They also should have fabulous intel, and counterintelligence that is unparalleled.
The Imperium as pointed out has to defeat each opponent quickly and not get into protracted war. This also means that they can't drive home actions like the Earth invasion or 'finish the job' in a total war sense.
So the key to the Imperium is rapid force shifting and reconstituting force quickly- a 'come as you are' war while a temporary surge is generated to turn the tide or perhaps push a little before a negotiated end and avoidance of the multiple front threat.
Another weakenss to consider is that the Imperium is more like a polyglot Persian Empire then a nation, and total effort may be hard to generate.
That's my thinking in part. The Zhodani are the most vicious and best military.
I'd think their leadership would be difficult or impossible to match if they were picking those who had significant telepathic, empathic, and other mental abilities that allowed their leaders to groupthink. It wouldn't matter if one or more were poor tactically on their own, as they'd simply rely on those that were competent to advise them real-time on what to do while receiving like information from the leader on the spot.
The Zhodani also have the advantage of being on a single front whereas the Imperium is surrounded on at least three sides by potentially hostile entities. The Imperium has no real tech advantage over the Zhodani either.
A further advantage is the Zhodani are far more homogenous as a culture and society than the Imperium. Their widespread use of psionics would make that a certainty.
Sure, the Aslan and Vargyr are never going to amount to much beyond a massive guerrilla war due to their social structures, but that makes them for all intents unconquerable. You'd have to invest in a huge occupation force to keep them in line.
On the flip side of that, they aren't going to mount a major war either. So, the Imperium would only have to maintain counter insurgency and anti-piracy forces along their borders with these two. Maybe a major fleet or two to back that up on occasion.
The Solomani would require serious forces, as would the Zhodani, for the Imperium to watch those borders. Worse, the Imperium is at the end of a very narrow corridor with the Zhodani.
The biggest problem for the Imperium is simply distance. It would take months for news of a conflict to get back to the leadership. It would take a year or more to send reinforcements from any distance within the empire. A J4 force would take that long crossing a sector, and J6 doesn't buy you much except the impracticability of taking much other than fuel and engines with you for a slight reduction in travel time.
So, the Imperium has to fight with what it has on the frontlines. That gets expensive in itself, maintaining large forces far from central authority. This in turn, regardless of canon, would mean most of the Imperial military would be equipped with low cost materials and technology rather than state-of-the-art. It'd mostly have to be a colonial police force rather than a top notch military simply because the later is unaffordable across the empire.
All of that would go with the "has to avoid a protracted war" scenario. The Imperium can't afford one economically or politically. They'd be forced to draw on their colonial forces which given the nature of their society with nobility ruling, would likely consist of troop loyal first to the local noble and to the Empire second. That would mean using them far from home would be very problematic.
All-in-all it points to the Imperium having a very hit and miss quality of military. There'd be an elite core of units that were very good, but the bulk of their forces would be pretty iffy in many cases often equipped well below TL 15.