Q:

What's the difference between 近々 and 間もなく?

I checked the Weblio sentences for 近々 and I saw this:

We are to start shortly.
近々に出発の予定です.

This reminded me of 間もなくwhich I often hear in trains. What is the difference between the two?
I checked some links here and here. What are your thoughts on this?

A:

Range of Time
近々 is in several days, months, or (possibly) years. I wouldn't say 近々 in several minutes or hours. 間もなく is used in wider range of time.
Relevance of Time
近々 can only be used as the 'soon' from current time, while 間もなく can be used with relative time.

そのチケットは販売開始から間もなく売り切れた

The tickets was sold out right after started to sell.

You can't replace this sentence with 近々.
Other Nuance
近々 also has a nuance like something coming.
間もなく often focuses on people who are waiting for something. It originally means "no time (to wait)". So in many cases, it's used for people to accept waiting for more seconds. "間もなく列車が参ります" (A train is arrived in a second) is very famous phrase in urban area of Japan.

