How is flambéing different from just adding alcohol?
What is the difference between just adding brandy to burning it with regard to taste?


Time and theatric impact (flambe is often done table side in a restaurant) are the big difference.

Flambe:


very quick, almost instant reduction of alcohol
texture/composition changes to dish are limited due to short process
visually dramatic
subtle changes in flavor


Adding alcohol, then further cooking:


longer cooking time to reduce alcohol
longer cooking will have a different effect on texture/composition
there will be changes in flavor, but in a different way from flambe


With most recipes, it comes down to time. If a long simmer to remove alcohol is undesired, you flambe. Example: Bananas Foster, if you simmered that for a long time, you'll get a hot bitter banana mush. Flambe is the better choice.

Without seeing your entire recipe: if your peppers are cooked a long time, you could simply add the alcohol and let the cooking reduce it. But if the recipe is a quick saute or similar, if you don't flambe, you may not get the flavor change the author intended. And, you may end up serving alcohol.