The biggest difference that I have seen regarding the Excel vs programming issue is the level of transparency that is provided in each. In excel, you get immediate validation of your functions and operations because you can see the results at each step. However, the formulas/functions themselves are 'hidden' and as the number of operations gets larger, it gets increasingly difficult to track and control the process. This makes debugging a nightmare. With programming, the results of your operations are much less transparent, but as you get familiar with the language you learn tricks to quickly summarize your data in ways that provide meaningful feedback for what you are trying to accomplish. More importantly, your script contains a concise record of all of the data manipulations and operations that you are performing, making debugging a much simpler task (compared to a monstrous spreadsheet).
An additional benefit to programming is that, after a certain level of familiarity with the language, your productivity increases dramatically. People using excel tend to be much more deliberate and cautious when creating the spreadsheet because debugging is such a pain, which means they tend to operate at a much slower pace. With programming, you can quickly pound out a script (often without even testing the various pieces of it) because you know you can easily debug the thing afterwards. From my experience, the difference in working styles results in almost an order of magnitude difference in productivity (what would take me an hour or two to create with a programming language could take a day or two to whip up in excel) and even with the extra deliberation/time, errors are still just as prevalent in excel. (And this doesn't even take into account the fact that it is much, much easier to reuse code than it is to reuse a spreadsheet).