Camera - Sony or Fuji Mirrorless

To start - I am a photography novice, never have owned a "real" camera. My wife is pregnant (no pics) with our first child and we do a decent amount of traveling (or we did before the baby). I keep saying that I'd buy a camera before the next trip, but never sat down to do the research. My wife being pregnant has changed that and expedited the process.

I am set on buying a mirrorless camera. I am also set on buying Sony or Fuji, but I can't make a decision on the body. Going into this process I thought I'd spend anywhere from $2,000-2,500 so the money is there for a body/lens in that range, but after doing research I don't think I'll need to spend that to get a camera for my needs.

Right now I am between the Sony A6000 and the Fuji XT-30.

Since I've decided on mirrorless, a Sony body has been first with Fuji a clear second, but the more research I do the closer it's getting. I have a few hangups on both and I wanted y'alls opinion.

I am buying this camera for landscapes and baby. Undoubtedly I'll be shooting more of the baby. One thing I have read is that Sony has an advantage on the Eye-AF and this makes a large difference in shooting portraits. How significant is this? This is a big hangup for me and the main reason why I haven't committed to a Fuji.

Another seemingly advantage to Sony is in post production. From what I have read, it is harder (not as smooth?) to edit a Fuji photo as it is Sony. I don't plan on doing a lot of heavy editing, but I do plan on doing some.

I really like the ergonomics of the Fuji. I went to a store last week and the Fuji was easier to handle and had a more natural feel to it. I have also read where the lens for the Fuji are much better than Sony's.

So, Sony or Fuji for a guy looking to take a few (a lot) of pictures of his kid/travel with an APS-C camera?

Thanks for any and all recommendations and opinions.