The difference is maintenance. With a rubber timing belt, it will be important to replace it about every 60,000 miles. Even though it may not be cracked, it will have become a little loose compared to what it was when it was new. This can cause small changes in the way the vehicle runs and can affect acceleration, starting and overall performance. Essentially, the car may feel doggy and hesitant. On top of that, it's way easier to plan for the replacement on your own terms than to be surprised by it. If the belt breaks while driving, vehicle stalls and you hopefully come to a safe stop. Or you go out to start the vehicle, it breaks while starting. Then you have a dead car and have to make all the arrangements to get where you need to be and get your vehicle fixed. The worst case, in a few older engines, is that the timing breaks and the internal engine components collide and lock up the engine. Then you are looking for a new engine or car. The average cost of replacing the timing belt and related components is about $800-$1200, depending on the vehicle.
Timing chains are more durable because they are made of metal. They do not have a recommended maintenance interval. However, there are tensioners and pulleys that these chains run on. If those fail, you experience the same issues as a loose belt. Sometimes the chains do fail. Again, that will lead to an engine that won't run. Timing chain replacement usually runs $1200-$2000 on average. Some are way more.
An important item to consider in timing belt replacement is the water pump. On many cars the water pump is driven by the timing belt. Therefore, replacement of one often means replacing both. The reason is, the labor cost is the same, so you might as well pay for the new parts and only pay for the labor once.
Like I mentioned, timing is everything. So I hope that this article came at a good timing for those who are reading it!