- 나중에 => later; at a later time (no practical limit to the time span). Broadly used with a somewhat vague sense.
- 이따가 => in a little while (limited to several hours in the same day). Colloquial term only used in conversation.
Also, 이따가 can't be used in the past tense while 나중에 can.
- 어려서부터 과학을 좋아하던 아이는 나중에 훌륭한 물리학자가 되었다. (이따가 won't work here)
=> The boy who loved science from a young age became a fine physicist later.