Matrix 1 Agents:
In Matrix 1 agents dress in a nondescript "Man-in-black" manner, and have common names. (Jones, Smith, Brown). The reason for this, is obviously, not to stand out.
Agents are programed as very power deprived in the grand scheme of things. Their speed and strength are just a notch above rebels. We see Morpheus putting up a decent fight one on one, first against Smith in the Matrix.
What kind of problems could a agent create from standing out? Well, when humans saw what resembled a human being invulnerable, disappearing into thin air, or being shot 20 times and standing, this created doubt in their minds. Increased the possibility of blue pills realizing that something wasn't right with the world - which was the trigger for the option that led to humans to become red pills. With enough doubt about the world they can even free themselves without any outside help, like we see The Kid doing in the Animatrix.
Seeing a Agent jumping or punching at unbelievable levels, it just didn't register as unlikely. People still had a hard time to believe they just saw that, but the more they stretched the power, the harder to suspend the disbelief it would be. A cop seeing a agent jumping, would just register it as almost impossible. If he saw an agent flying or ghosting out, then he'd know it was impossible.
And people did see agents fighting against rebels all the time. At the start of The Matrix, Neo is scouring the Internet for news about Morpheus and we see stories of him evading police in some airport.
Matrix Reloaded / Revolution Agents:
The agents do get an upgrade as Neo notices fighting them by the start of Reloaded when they almost manage to hit him, but they are still severely underpowered next to Neo. They have larger bodies, and are taller. Their names are longer, and end in "-son" (Jackson, Thompson, Johnson). The purpose of this upgrade seems to be, to hunt The One, but they are still severely underpowered, and no-where near the power level of the older version. They still look and act like humans.
Morpheus ends up fighting and killing an upgraded agent to save the keymaker.
Alpha/Beta Matrix agents:
We get to see older versions of agents, at least one specifically, but possibly more. Seraph is confirmed in The Matrix Online (TMO) to be an agent from the very first version of The Matrix, where agents were known as Seraphims (a Seraphim is a rank of angel). The first version of the Matrix was described by Smith as:
(...) the first Matrix was designed to be a perfect human world where none suffered, where everyone would be happy? It was a disaster. No one would accept the program. Entire crops were lost. Some believed that we lacked the programming language to describe your "perfect world". But I believe that, as a species human beings define their reality through misery and suffering.
In TMO the first Matrix is called "Paradise Matrix", so having angels as agents is fitting. On the sequels we find out Merovingian saved Seraph, and Seraph eventually turned on him. But more importantly, we see Seraph going one on one with Neo, and putting up a fight - which shows the power level of the very first agents. On TMO, it is stated he is the strongest entity in the Matrix, second to Neo alone - but we already see a semblance of that when he fights Neo in the Reloaded.
The version right after Paradise Matrix, is called Nightmare Matrix in TMO. The architect describe it as:
I redesigned it based on your history to more accurately reflect the varying grotesqueries of your nature.
That's where the Ghosts, Vampires, Werewolves and Aliens in the employ of Merovingian come from. Again, they are much stronger than your regular agents with a multitude of powers that make them extremely hard to kill, from disappearing and going through walls, to being unkillable without silver bullets. Persephone describes them as:
They come from a much older version of the Matrix, but like so many back then they caused more problems than they solved. My husband saved them because they are notoriously difficult to terminate. How many people keep silver bullets in their gun?
The Oracle goes on to describe how the Matrix handles these unlikely sightings of power:
Every time you've heard someone say they saw a ghost, or an angel. Every story you've ever heard about vampires, werewolves, or aliens, is the system assimilating some program that's doing something they're not supposed to be doing.
This shows the system tries to mask the actions of super-human programs by trying to provide a believable explanation. The wilder the action, the harder it is to explain. Most people will have a hard time believing they saw a ghost - creating doubt in their mind.
The agents used to be very powerful, and we see a very clear scaling down of power. From Seraph to the Ghost twins and the other monsters, to the current agents. Even when the current agents get an upgrade they are still weaker than older ex-agents. Each iteration of the Matrix tries to do one thing above all, to make connected humans accept the program.
The first version provides a perfect world and fails. The second forces the programing and fails as well. Eventually the oracle finds the problem is choice and the modern Matrix is born, with modern protectors. As the architect puts it:
(...) she stumbled upon a solution whereby nearly 99% of all test subjects accepted the program, as long as they were given a choice...even if they were only awar e of the choice at a near unconscious level.
The problem with choice, is that people will become aware of it the wronger the world feels. Morpheus describes that feeling as:
You're here because you know something. What you know you can't explain, but you feel it. You've felt it your entire life, that there's something wrong with the world. You don't know what it is, but it's there, like a splinter in your mind, driving you mad.
So, in the Modern Matrix, people are given a subconscious choice. The problem, is that the world must look "real" and "normal". If you see something that leads you to question the world, it can very well lead you to becoming a red pill, and they don't want that. So as a way to prevent that, agents are very limited manner. They can't fly like Seraph anymore. They can't ghost out, or take 10 bullets to the chest and survive.