Life in the Roman city did not resemble modern urban society much at all. The vast majority of urban dwellers were migrant day workers living quite literally a hand-to-mouth existence. Hourly pay, to say nothing of minimum wage, was a concept totally alien to the Roman world, where the vast majority of workers searched daily for work, often in vain, and were paid wretchedly for it. The three denarii per day that Cicero claims even a low slave could earn, which is almost certainly quite idealistic, was barely enough to support a single individual after the cost of rent (extremely high in the city, and often paid daily, meaning that a large portion of the city was more or less semi-homeless) and food, and was nowhere near enough to support a family. Urban dwellers live, often temporarily, in conditions that sound similar to the modern apartment block when initially described but are totally unlike anything outside the third world. There were no building codes, and insulae were often built of rubble with a thin facing of stone, with shared walls to save space and money. Besides catching fire, which would spread easily due to lack of space, insulae were constantly collapsing due to poor building methods. Most families in an insula shared a single room with little light or space, and none of the amenities of a modern apartment like kitchens or bathrooms--the average laborer of the urban poor would be shocked to learn that even the modern working class can manage home-cooked meals. With constantly fluctuating grain prices and the possibility that you might not find work that day there was no guarantee that you might have the money to buy enough, or any food, in which case your family went without--grain laws did something to alleviate the situation, but they were not welfare and were not enough to feed a family. Most of the city lived on the edge of starvation in horrible malnourishment, which the filthy living conditions of the city did not improve. Despite the excellent public sanitation of the Roman world most people lived in squalid conditions. Disease was constant, and with the enormous rate of immigration within the city new diseases were constantly being brought into the city--the death rate to disease was terrifyingly high.

Since you mention "political parties" I should make this clear: the Roman world knew nothing remotely resembling a political party. The tired and abused mis-statement that the optimates and populares were anything like political parties is the uninformed belief of writers who know little about Roman politics. The average Roman citizen, who did not necessarily make up the majority of urban dwellers, was a part of a political system totally unlike our own. The degree to which the Republic was "democratic" is hotly debated, but much of the urban plebs probably had little ability or interest in politics--how much is a matter of opinion. Most of the urban plebs were in the lower property classes of the comitia centuriata or were part of the capite censi, whose votes were essentially worthless and who probably rarely showed up to the vote in great numbers. The urban population was a mix of rural dwellers migrating into the city either permanently or for seasonal work and actual members of the urban tribes, of which there were only four--even in the comitia tributa the urban tribes had little influence, even though they made up the majority of the population, as they only had four votes compared to the thirty-one rural tribes. With few urban dwellers able to afford to miss a day's work to attend contiones or elections much of the political activity among the urban plebs was probably restricted to a fairly small group--if the capite censi even bothered (or were able) to vote they had no reason not to vote according to a candidate's influence alone

There are many more differences that I could rattle off, and ultimately the similarities between the ancient and modern city are largely superficial. This is not to say that similarity did not exist--the Roman city was decidedly urban, commercial, and cosmopolitan to a degree that would not be marched until the modern era in the western world. The life of shopkeepers and tradesmen, a privileged minority of the urban plebs, would not be so different, nor would the lives of rich who could afford good sanitation and real living conditions. Even then, though, existing in a pre-industrial world lacking the Scientific and Green Revolutions would have made such a great difference that arguably the similarities to our own lives would largely be no greater than the differences

EDIT: I feel compelled to point out the obvious, that this of course refers to city dwellers. The majority of the Roman world lived as relatively poor farmers, a condition not too unlike that of many inhabitants of rural Italy today but which would be pretty alien even to a lot of American farmers, to say nothing of the urban-dwelling American majority