I believe the main answer is simply the amount of ruins in the city. Or, in another terms, the size and importance of the city in Roman times.

Rome, as the capital of the Empire, would have by far the biggest amount of monuments that can survive to the present day. In comparison, London and Paris, which were relative big cities in the context of the Western Empire, were small compared to Rome (I believe both had between 10.000 and 50.000 habitants). And so, the number of major buildings that tend to survive for so long were smaller. Yet, we can still fight them above ground: The Roman wall in London for example, which for the vast majority of the city history served as the limits of the urban area. Or these Roman Baths in Paris. The opposite is true for Rome, you can find underground ruins, although at the moment I can't think of one in particular. But the underground of the city is full of history.

Another important aspect is how the city was occupied throughout history. Buildings survive not simply because they were well built, but because they are preserved. Many Roman structures only survived to this day because of this.

Your question would be best answer if we look at individual buildings and try to see the history of its use and how that part of the city was occupied through time. Sometimes even in ancient times we can have cities changing considerably in shape because of new situations or disasters.

A lot of Romes ruins are underground still. They have been trying to expand the subway for years but keep running into undiscovered ruins plus even places like the forum are below "modern ground level". Due to constant flooding of the Tiber river the modern city is quite a bit higher than ancient Rome.

During the middle ages Rome was mostly abandoned, whereas both London and Paris started to grow. So while Roman buildings in the forum were being abandoned, in Paris and London they were used for making new buildings.

Then you have to consider the modern period. For example, during the XIX century, most of old Paris was demolished to make way to the boulevards and buildings which currently can be found there. In the other hand, during this same period, in Rome the old middle ages buildings where demolished to give way to most of the Roman Forum that can be found today.

A very clear example are the two churches (Basilica dei Santi Cosma and Damiano & Chiesa dei Santi Luca e Martina), in the Roman Forum that weren't demolished because they're religious buildings.