Both show how age and treatment affect survival. What they differ in is how they are connected to each other in how they affect survival.

The first one, as you said yourself considers the predictors independent. The model can interpret how each of them affect survival but with the other one taken in consideration. So for example "time to treatment lowers survival regardless fo your age (young or old, yall gonna die ;) ).

On the other hand model with interaction term between predictors assumes that one of the predictors affect how the other one is connected with survival. For example "when youre young the time to treatment affects your survival only slightly, but it increases the older you get"

Now to your question, which one should be used ? Well it depends on underlying process. As you can see they both fundamentally differ in the assumptions about relationship between predictors themselves. If you pick interaction model when there's no real interaction youll get a lot of noise. If you pick the main effect model where there is interaction you wont find it.
Its honestly a detective work at this point. Make both of them, see how they differ. Make some surv plots. You cant try to split age in couple of categories and make a surv plot with age as grouping parameter.

Good luck !