I has the same situation. I got the note 10 plus and could not be happier I showed this to apple fans and they were so jealous of the gorgeous display, customization, performance and battery life.
Well... if battery is your biggest concern then go with the 11 max pro. But if you wants all the coolest features like, a bluetooth stylus, wireless powershare, more camera features. Then get the Note 10+. Also, why are you asking about 1000$ phones when your picture makes you look 7?
Get both phones that way you set up both and have it ready. Put your sim into one and use it. Put your sim into the second phone and use it. This is what I do. I used to have 6 phones at a time and all of them were flagship phones. I then decided to sell most of them, but do have Pixel 2, iPhone 6, Moto X and Note10, not including my nokia feature phones
Note10 all the way. Apple feels more of a fashion statement than a do-it-all device. I actually get people wowed by charging their phone with mine, and a stylus too. I recommend the Note10. Or Note10+. I own the Note10+. You can ask me anything about it. I've had it for a month now, and I enjoy it a lot.