[General] play with vs play on

[maoyueh]

In the following sentence, which is the better choice, or are both correct? Thank you so much.

My son spent a lot of time playing (A. with B. on) his mobile phone.

 

[Phaedrus]

To me, each has a different connotation. Playing on one's phone could mean doing things like playing video games on it.
Playing with one's phone has a much less sophisticated connotation. It could mean, e.g., having fun turning it on and off.