Well I have an example I use that shows the 10-year mortality rate between two treatments is the same, but the rates across time are drastically different. Since the placebo group all dies within 2 years and the intervention group dies about 6-8 years post exposure. Thus a cross-sectional comparison misses this difference. How, perhaps your outcomes are immediate, which would make this a mote point.
@Karabiner - it is hard to control for this even if you have discete time intervals for data collection without using survival analysis. However, you could add time to a multiple variable regression to try and remove its effect.