It's a superpowered guy-in-a-suit matchup!
The Observers are technologically modified humans from the future - they can teleport, read minds, catch bullets with their bare hands, travel through time, see spatial distortions with the naked eye, and possess superhuman strength. They also have incredibly advanced technology that can open larger portals through time, rapidly age a person, etc. When they use weapons, they tend to prefer a sort of pulse pistol that knocks everything in a cone back with great force. In Season 4, they
Their mind-reading can be resisted (either by misdirection or by massive force of will) but it is a taxing process that leaves the target at best, drained mentally, and at worst, kills them. Likewise, weapon technology developed in the Fringe universe has produced a small amount of special guns that can fire a bullet faster than an observer can follow it, which is as effective against them as a normal gun against a normal human being. Observers also have sweet hats.
The Agents are programs that bend the rules of their virtual universe - they have incredible strength, are fast enough to dodge bullets, and can never truly die so long as they can possess a new human host. The only way to defeat them within the Matrix is to break its rules even more; normally, only The One is capable of such a feat. They have awesome sunglasses.
The Observers, using their parallel universe shifting powers, discover the Matrix world, which behaves just like a normal universe for plot reasons. They don't count "jacked in" to the Matrix, and possess all the powers they normally do. They can leave it whenever they want the same way they got there, without needing phone lines. They decide to conquer it, because that's how they roll. The Matrix detects an incursion, and Agents are able to duplicate the technology that the Fringe humans used to travel between universes (a permanent corridor with checkpoints on both sides, and an impromptu method that switches an equal amount of previously tagged matter from the same location in both universes). They do not use the other universe-shifting tech, as it would destabilize the Matrix and risk waking up or killing all of its human hosts. While the beachhead for the corridor is secret for now, Agents are vulnerable in Fringe-Earth because they don't have access to their host-shifting abilities. If they die there, they die permanently. Because that Earth isn't screwed up, though, they're interested in taking over it for the solar power and other resources.
Without making contact with the resistance on Fringe-Earth, Agents cannot develop Observer-killing firearms.
Observer pulse guns can't be dodged by an Agent, but only do enough damage to stagger one.
Main characters from both sides are out of the picture - they're off having main character adventures. This includes the Architect. Nameless resistance fighters on both sides are allowed, though.
The Agents don't get to just program in "a really cool robot that totally blows up everyone" and push it through the portal. They're limited by their programming to the tools they normally have at their disposal.
The Observers don't know the location of the Agent beachhead...yet. They haven't set up their own gateway in the Matrix yet, but they can create temporary gates with no difficulty, so it's not a priority.
In a one on one fight, who wins between an Agent and an Observer? The Observer running away via teleportation counts as a loss unless he comes back to finish the job.
In a war, will the Observers conquer the Matrix, will the Agents be able to take the fight to Fringe-Earth and win?
If the Agents manage to import their Sentinels into the Matrix, and send them into Fringe-Earth from there, would that make a difference?