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It's a solid workhorse for the fact it's already 4 years old! The colors are dynamic and it was definitely a huge step up from the D7000 I used before. Sure, Nikon brought out the D850 last year which I think could outrun the D750 in terms of performance but I don't really know – Need to test it out for more than a few hours.
The company I work for has a few of the D750's in all of their photo studios in Germany & Austria. So yes, it's a very reliable camera.
Besides the 24-70mm I also use Nikon's 50mm, but I can't recall the last time I actually used it...

D850 should be a bit better but I'm not sure if it justifies the change in price. It's overly pricey in my opinion. Are you happy with video on D750 as well? I will need to take a few..

I've heard that many people use 24-70 and it's kind of an all-rounder so I might just settle for this one as well..

I haven't really used it for video except that one time two years ago I shot a DIY music video. It was quite OK for the circumstances, but I'm not much of a film-maker though.

I think this video showcases the video-making qualities quite well:

Thank you! This is a very positive review. I still have to decide if I'll go with a Nikon 24-70 or Tamron 24-70 lens. I know that you shoot with Nikon but would you ever consider changing to Tamron?