So guys, this was something that was crossing my mind. I myself have multiple platforms, but when multiplats are released I tend to have a preference for one console over an other. I try to get games for the PlayStation console unless there are certain exceptions. In any case here are some possible scenarios I can think of:

1. Brand loyalty - Choose the console that is mainly in your brand of choice
2. Performance - Choose the best looking/performing version of the game
3. Price/Availability - Choose whichever one you can find/the one that is the cheapest
4. Genre - Some people prefer controllers for some genres while KB+M for others which would affect their decision
5. Exclusive content - Choose the version that has the most content/has a special edition, etc.

I own all three. The Switch is for Nintendo exclusives. PS4 is for Sony exclusives and Xbox One is for Xbox exclusives and all multi-platform online games.

So, what about the SP multiplats?

I've always owned pretty much every console on the market since the 6th gen.

For me, it always went like this:
-Exclusives for each console (of course)
-Best version available of the hardware I own.
-If there's no performance difference, get the Xbox version.
-Final Fantasy, Metal Gear, etc. (Certain games that just "feel right" on PlayStation) get the PlayStation version.
-If it's a good port, get the Switch version in addition to whichever version is the best version.

Last gen, I almost always got the Xbox 360 version of multiplats. This gen, I got the PS version-- up until the Xbox One X released. Now, I get that version. If there's exclusive DLC, that makes a difference too. I always go digital and, more often than not, if a game is on sale for one console, it's on sale for the other at the same time or soon after.

I get which ever version runs the best. That usually means PS4. But if there's any online component at all and I know I'm going to be using it a lot, I will go Xbox One even if it runs worse. 

I suppose it'd be brand loyalty for me since at the start of most gens I'll only have 1 of the 3 consoles available, with a 2nd console bought later in the gen for exclusives mostly.

There was an exception when I have both a GC and PS2 in the middle of that gen. So I bought whatever version of a game I found 1st, which resulted in mix-matched 3rd party games.

Own all three platforms, Switch, PS4 Pro, and Xbox One X.

I have always bought Multiplats on PlayStation due to their commitment to new software (first party), and new ways to play (Eye Toy, PS Move, PSVR).

Really depends on the game. Getting an indie/mid-tier game on PC feels like an inferior version since the Switch is portable and those games don't depend on graphics. Hollow Knight isn't going to see a huge graphics upgrade on a 4k tv. Big budget 3rd party games depend. I like playing big RPGs portably since I can grind at school or outside of my home. FPS I will get on PC unless it has local multiplayer.

Well for the most part, I grab all multiplats and exclusives that itnerest me on PC.

I usually fit them under:
Price
Content
Performance
Visual qualities
length of play

With the Switch, I'll go for it's exclusives (for the small number I like playing), but I'll sometimes grab multiplat titles that I had previously bought on PC, though that depends on the price (especially with Nintendo's e-shop) and performance.

I look at the game.
I think "Is it on the PS4?"
Then I buy it on PS4.

JK if it's single player and not Dark Souls with 60fps, then Switch. If not, PS4. XBO is really just for extra space, but I haven't booted it up yet.