I guess کردن is much more commonly used, while the other is used more formally.
Also, انجام دادن somehow implies to do and finish something, while کردن usually just implies doing it.
Another point is that کردن can be combined with other words to make many new verbs, such as: گریه کردن = to cry, تکرار کردن = to repeat, پیدا کردن = to find, مخلوط کردن = to mix, خرج کردن = to spend, فرار کردن = to run away, etc.