Qaislaz Zubaidi is eating lunch with his family in a pleasant park on the banks of the Tigris. He asks me to join him and we watch as a pair of scullers from the Iraqi Rowing Union sweep past on the river's brown current. Zubaidi, 47, is in real estate and successful by the look of him. He is a member of the Shia sect; 10 years ago, he was an officer in the defeated army of Saddam Hussein, his city newly under US occupation.

"I didn't give up until 11 April, two days after the fall of Baghdad," he says smiling. "There were only four of us left. The radio had gone silent. There was no communication. No one to ask for orders any more. We sat down and decided things had come to a dead end. So we left. I didn't feel relief or anything; I just felt negligent for abandoning my post. Then I got home to chaos and looting."

Zubaidi talks without bitterness. He tells me he is happier these days and hated his time in the army. "Under Saddam, the state intervened in everything. We were ruled with an iron fist. In those days, I couldn't afford fruit and didn't have a car. Now everything's reversed. We have freedom. We can buy what we like.

"But," he continues, "we don't have stability. The politicians here behave grotesquely. They are climbing on the people's shoulders to benefit themselves and I blame them too for the sectarian instability that we have here again."

We chat a little longer. It is only after leaving Zubaidi and his family that I think about arriving in Baghdad on the day the city fell – 9 April 2003. I remember how, although I'd seen many US and British soldiers over the days of the US-led invasion, by the time I arrived in the capital, Iraqi soldiers such as Zubaidi were gone, their uniforms abandoned in little piles on street corners. In the southern city of Basra, which had fallen a few days earlier, the only Iraqi fighters I came across were the bodies outside the university that locals had covered with carpets. It has taken me 10 years to ask an Iraqi soldier what defeat felt like.

I missed the start of the invasion of Iraq. I was on the wrong border at the wrong time, but I quickly caught up. Reporting for the Observer, travelling independent of the invading US and British forces, I found myself by chance walking into Basra on the day it fell to coalition forces. I followed a British paratroop column I'd run into on the road, waiting to enter the city. Travelling with a couple of colleagues, we continued when the paratroopers stopped and reached the Shatt al-Arab waterway on the city's edge. On the banks, we found a parade of eerie figures, statues of soldiers with fingers pointing towards Iran.

A few days later, the evening Baghdad fell, I was on the outskirts of the Iraqi capital, driving past burning buildings, US tanks and the scattered bodies of Saddam's paramilitaries – fedayeen – and civilians. That night was spent in the grounds of the blue-domed mausoleum built by Saddam just a year before to commemorate Michel Aflaq, founding father of the Ba'ath party. We were invited to stay by occupying troops of the US 3rd Infantry Division after an awkward incident in which they almost killed us.

For four years I kept returning, to cover the first elections and then the first wave of sectarian killings that started in the Baghdad suburbs. In time, sectarian conflict would sweep across Iraq, introducing an era Iraqis call the sectarian war, which pitted the Shia militias that had infiltrated the police against their Sunni rivals. Al-Qaida got involved, bombing Shia shrines and pilgrimages, fuel queues and weddings. Over three years, from 2005 to 2008, whole neighbourhoods were "cleansed" and tens of thousands killed.

My last two trips, in 2007, were to report on the US military "surge" in Baghdad, when President Bush increased troop numbers in an effort to stabilise the city. This was the beginning of the end of the worst of the sectarian killings. I twice found myself in convoys hit by Sunni jihadi-militant bombs. The first time, in the city of Baquba, four Iraqi soldiers were killed. The second, on the way back from the town of Tal Afara, a car bomb detonated in front of the US armoured vehicle I was travelling in. It seemed time to take a break.

The first thing I notice, walking around Baghdad today, is that there are street vendors with their drums of embers preparing and selling masgouf – grilled carp – on almost every pavement. Ten years ago, if you could find it at all, the national dish was only available in the restaurants in Abu Nawas Street, which catered to the old elite. One of the vendors explains that the proliferation of artificial ponds for rearing carp has brought down the price. What was once expensive has become available to all.

Driving around one afternoon, an Iraqi friend points out a poster hanging from a lamp-post for the provincial council elections in April. "See that," he says. "It reads 'my province first'. In Arabic, the word for province is 'muhafatha'." He giggles. "If you remove the 'alif' [the long Arabic 'a' after the 'h'] it reads 'my wallet first'." A wag, he tells me, has already made this amendment on Facebook.

Later, when I visit the human rights activist Hanna Edwar, she will tell me that while her country may now have the appearance of democracy – elections and political parties – it lacks the functional realities. It is beset by corruption, nepotism and an often scant regard for the rule of law.

The most visible sign of the corruption afflicting Baghdad is the state of the pavements. On every block, you can find a section dug up and waiting to be shoddily relaid by contractors who – so the story goes – bribe local politicians for contracts to renew the streets almost every year, whether it's required or not.

Still the city has improved. The Baghdad I left behind five years ago was a grim place. Even short journeys out of the Hamra hotel, which would be bombed twice and now is almost derelict, were dangerous. I recall one evening sitting there and watching a fireball erupt as a neighbouring hotel was hit. There were random checkpoints and militia in the streets, boys on motorbikes who, if they saw a foreigner, would phone in the tip for money.

These days, Baghdad can be a vibrant place, its parks crowded and its restaurants busy. There are new shopping centres under construction. You see Range Rovers and Lexus sports cars. One day, I saw a cyclist in full Lycra on a Bianchi racer, powering through the traffic. But the sprawling, less well-to-do neighbourhoods, such as Ghazaliya, Dora and Saidiya still feel angry and tense. The concrete walls and armed checkpoints, put up during the American occupation at the height of the sectarian violence, remain in place. They still function to control the population, limiting access in some neighbourhoods to a couple of exits that can be easily sealed off.

And although the private security contractors who would fire warning shots to clear the traffic are gone, and US soldiers no longer patrol the streets, Humvees and armoured vehicles remain on every corner, repainted and manned by Iraqi soldiers and police. There are still killings related to corruption and politics almost every day – not on the same scale, not civil war any more, but a steady drip-drip.

The same tall concrete blast walls still surround the green zone, the name US officials gave the city centre area, with its palaces, government homes and foreign embassies, to differentiate it from the dangerous red zone outside. In places, the walls have been painted on, but that does not change what they are: fortress walls built to protect the buildings inside from the bombs that still target them from time to time. I go looking for the people I came across during previous times in Baghdad. And I find no one who has been left unscarred by the last decade.