Comparing to the (rigid, stiff) chain, the (soft, flexible) timing belt has 1 very important but relatively hard to explain attribute which makes it much better than the chain in doing the timing job.
During normal operation, the timing chain's movement itself is actually not a smoothly continuous action; this is owing to the fact that the chain is composed of a lot of "segments" that are connected together, rather than being a single piece of pulling media like the belt or cable.
The slackness (or tightness) of the forcing side of the chain changes periodically as each single segment of the chain is rotating by. It works in a rhythm of "tight-slack-tight-slack-tight-slack....." with the peak force existing somewhere during each of the tight-slack cycle.
The peak force periodically appears but exists only for a very short time interval as the driving shaft is asserting force to the cam-shaft.
Mathematically, this kind of stimulus (driving force) is modeled as the well-known "delta function". Delta function is very special: It is the only kind of stimulus that can stimulate the full-range-spectrum of frequency of the system which is being excited by it. A college boy/girl of the electrical engineering school more likely need to deal with the delta function in circuit classes during the last 3 years of his/her school days.
To put it in a simple way, a short pulse of electrical driving voltage and a quick hit/knock of mechanical force are both qualified as "delta function stimulus inputs".
Most people have at least once heard the bell ringing in a church or chapel, but few would realize that it is a very good example of the "delta-function stimulus" system.
No matter what sound a specific bell will generate, the sound is generated by a hammer hitting/knocking the bell in a "very short time interval". Because this "very short time interval" of acting duration, this kind of stimulus matches very well to the "delta function" definition. And for the same reason, there is no way that the generated sound frequency of the knocked bell could ever be some how controlled/instilled by the hammer's action (the hammer just does not "have time" to do the instillation). Rather, the pitch of the sound is exclusively decided by the character of the bell itself.
The hammer's "delta function style" force stimulates the full range of frequency, but since the bell was designed to have a very special and narrow resonant frequency (also called the nature frequency, characteristic frequency), only this specific frequency get resonant (kind of amplified) and emit the corresponding sound, the other part/frequency-range of stimulus force just get damped out. That is why the dozen of different size bells hanging up in the chapel's tower, each gets hits by a hammer in the same way, yet, they generate sounds of pitches different from each other's.
If the other way is true (that the knock of the hammer does not cover full-range-spectrum of frequency, rather, one specific hammer will only offer knocking force of a specific frequency), then using the same hammer to knock several different bells, there shall be only 1 or 2 bell that is/are ringing, all the other bells will be dumb after being hit by this same hammer; which is of course not the case.
Off track long enough, let's go back to the timing chain issue.
When a car is equipped with the timing chain, another source of jerking force will further enhance the delta-function effect: The internal combustion engine by itself is not a continuous force source, which is obvious. Hence, the driving force of the crankshaft itself is also a delta function. The net effect is that a delta-function mounting on top of another delta-function.
What will this mean to an engine? Whenever the engine is running, the timing chain will tirelessly stimulate the engine block through the sprockets bearings with delta-function force that cover full-frequency-range. Sooner or later, any fixture, frame, block of the engine that has its nature/resonant frequency covered by the delta-function will be exuberantly vibrated (also known as resonant) to loose, especially those parts that is located close to the timing chain. For example, if a water pump has been designed to reside around the timing chain, very likely this water pump will get leak much earlier than it would do with a timing belt design --- and not because the failure of the pump itself that causes the leak, but that the good pump has been shaken loose from the engine body. Nissan Altima V6 has long been suffered from the coolant and oil leaking/dripping problem; it happens that the Altima uses timing chain since the very first version.
Shaking-until-loose by the chronic knockings of delta-function force is more severe if the engine body is made of cast iron instead of aluminum alloy. This is because the aluminum is not as stiff, rigid as the cast iron; more or less the jerking force is absorbed better (because the distance between the sprockets axis are not that strictly constant) in an aluminum engine block than it would be in the cast iron one. Decades ago, when cast iron was the only choice in making engine block and timing chain was the only player in the town, Dodge car had been laughed as vehicle of "Drop Oil Drop Grease Everywhere".
Contrastingly, belt is flexible; it will relax, stretch or shrink to absorb the jerking force. Therefore there is no relentless jerking force like the one described above that is incurred by the timing chain. Additionally, quietness is the well-known virtue of the belt.
The drawback of belt is that it must be changed strictly abiding by the maintenance schedule to avoid the catastrophic failure. And the maintenance fee is relatively high.
I would bet that the car maker will always put timing belt in their high-end (expensive) models; like Lexus is to Toyota, and RL/TL sedan is to Acura. How about the low-end/entry-level models? Well, if a customer is not rich enough to buy a high-end car, he is not likely happy to pay the timing-belt changing fee either; instead, he would risk the belt failure to save the dollars. And when the catastrophic failure does occur, he will be another upset customer. On the other hand, when one is financially stringent, he is more inclined to learn how to tolerate the noisy chain. In recent years, both Corolla and Civic adopt the timing chains; they are the foot-print of this strategy of the car makers: Since you pay the bill, I will offer you what you want; even though the other way which you don't like might be a better one.
I also speculate that after the Civic adopting the timing chain since 2006, oil/coolant leaking problems (especially oil leak between engine head and head cover), oil (dripping from seal between the plug tunnel tube and head cover) fried around the spark-plug, cam-shaft mountings loosing, valve-clearance error issue, cam working surface lubricant insufficient… and etc would happen much frequently and prematurely. None of these problems is fatal to a car; accumulated and delayed to fix, however, will shorten the life expectancy of a car significantly. Failing to remove the fried oil deposit around the spark plug before taking the plug out, for example, will get the fried deposit, accompany with dirt mixing among them, falling into the cylinders. This foreign particle is very good grinding material in grinding your piston rings and the cylinder wall. Therefore, a 300,000+ miles reading in the odometer of a Civic version later than 2006 might not be as common as those Civic generations prior to 2006.
Theoretically, if it must use timing chain, a 4 cylinders engine is better than a 6 cylinders', and V6 cylinder is better than an I-6 engine. That's because the resistance force of the cam-shaft is relatively lighter in the 4 cylinders and the V-6 engines (I assume that the V-6 uses 2 separated timing chains, rather than 1, hence the delta-function force are evenly distributed), and hence the delta-function force is weaker in these engines, and less likely cause trouble.
