Home piano and stage piano are two completely different animals.
A "home" piano is designed to be permanently set up in the home. Therefore it must be aesthetically pleasing because it may well become a focal point of a room in your home. To that extent, more energy and expense goes into the way it looks. A piano on stage is not usually front and center and nobody is concerned with the aesthetics as much as functionality. Also, since sturdiness is more important than weight the built in integral "stand" on a home piano will be far more substantial. So you have extra money in the infrastructure.
Furthermore, a home piano will not be plugged into a PA system so it must provide it's own sound. So to that end, a home piano must incorporate a sound reinforcement system (small built in PA if you will) that is capable of reproducing a pleasing sound and delivering the sound to an audience - in the absence of any external amplification. Many "home" pianos are designed with beginning pianist in mind and may incorporate learning software into their design which could also add expense.
A "stage" piano is an "instrument" designed for a professional musician to use in public performance on stage. It is envisioned that such an application would entail plugging the instrument into a PA system or keyboard amplifier. Thus very little expense need be devoted to internal amplification and sound reproduction - since that will be handled externally. Because these instruments are designed primarily for more pro level musicians, they need not contain any of the learning software.
If your interior designer does not object to the way your piano fits in with the room decor - and you have no desire to invite guest over for home recitals, you will likely get more value from a stage piano generally speaking.
If aesthetics are important and you want to entertain in your home without the need to set up an external amplification system in the room where your piano lives, then a "home" piano might be the way to go. But be prepared to give up some of the features that a professional musician might find useful.
Having said that, you should also consider other factors that are important to you and that you might likely use. The feel of any digital piano will differ by manufacturer and model. Some do a better job of creating the weighted hammer action feel of a real acoustic piano than others. You need to play them to determine how you personally like the way the action feels.
Also, many home and stage pianos may contain features you will never use. Will you ever use a large library of sound samples or use features such as split keyboards and the ability to layer sounds one upon another to create unusual effects? You might not want to pay extra for features you are not likely to take advantage of.
There may be some features that you will find very useful. If you want to plug in headphones for silent practice, be sure the piano you choose allows this (most will). Would you use a transposing feature? Would you every use any form of auto accompaniment? Is both MIDI input and output something you will find useful?
You might want to make a list of the features you feel would be useful to you to be sure the piano you choose offers most if not all of those features that are important to you.
Regardless of which piano you choose, I hope you derive great joy and pleasure from playing it.
