Photos: discrepancy between iTunes and Photos

Hello, I have a long time going issue with the discrepancy between the number of photos I have in Photos and iTunes. Here is the scenario:

I take pictures using my iPhone, then sync it with my Mac Book Pro. Photos showing let's say 10,000 photos/videos

Go to iTunes and it shows 9,935 (usually a small bunch less). So when it gets synced back with my iPhone, I have a few pictures less.

After a few days delay, these "missing" photos appear on my iPhone just fine (after sync) but another, new batch of freshly made/synced photos are being "lost".

In other words, there is some delay in sync between iPhone>Photos>iTunes>iPhone.

I've tried to deal with it by calling Apple support, and they've done three sessions (about a year ago), but couldn't resolve the issue promising each time to call again. The problem is - I'm always on travel for work, and it's hard for me to be available for Apple to give it another try...

I use my iPhone for work, taking lots of pictures. Having it syncing properly is critical. Please help.

Sincerely,

Anatoly