Your stove is a significant factor in whether a wok is worthwhile versus a flat bottomed pan.
Woks benefit from very high heat. Some people think you need a professional stove to use a wok properly because a residential stove heat output is too low. There is a characteristic wok hei flavor that is a result of using this heat that probably is not reproducible with a residential stove.
A wok does not have the heat capacity of a cast iron pan because it is relatively thin. You can preheat a cast iron pan for awhile before cooking to sear, but this does not work with a wok. You need to continuously apply high heat to sear in a wok.
With an electric stove, I prefer to stir fry in a cast iron pan over a wok, while over natural gas, I prefer to stir fry in a wok. Over an electric stove, you need to divide the cooking into small batches to prevent your stir fry from becoming a simmer/boiling. I have no firsthand experience with induction stoves, but I have heard they are better than electric for use with woks.
To summarize, if you have a high heat stove, consider a wok. Otherwise get a pan.