1. As fas as we know, Nintendo NX ( next generation Nintendo console ) will be a handheld with Xone-level ( Microsoft current gen home console ) specs, using AMD ( PC, Console Hardware creator ) tech, what is used already in PS4 ( Sony current gen console )/X1. Everybody knows multiplats ( Games released mostly on PS4/X1/PC) sell the most this gen, so it is obvious, necessary and mandatory move. They held some meetings with EA (3 rd party games publisher ) already, and NX is rumored to be super-easy to port games from X1/PS4/PC.

Long story short - Nintendo will get full 3rd party support, if only moneyhat enough/sells enough consoles. 

2. Exclusive deals with 3rd party are now a single-digit thing, it's mostly timed exclusive ( play it first scenario ) or exclusive DLC ( exclusive content released digitally, but nothing earth - shattered ) . Moreover, the games that are already released as 3rd party console exclusive , bombed hardly ( Sunset, Tomb, D4, Rise, Street Fight 5 ). The ones that are announced as 3rd party exclusive, like Scalebound or Shenmue III, hardly can be considered as a future system-seller. Common architecture makes porting games super cheap, so in fact u only lose money/fanbase/ opinion, if u are 3rd party involved in the process.

Long story short - 3rd party exclusives, little by little, will be a song of the past.

3. Gen over gen, consoles are becoming more familiar to each other ( remote control, companion app, online services, Blu Ray disc, mandatory install etc ). Moreover, overalll console businnes model has changed - super risky moves, like PS3 Cell CPU or always-on, mandatory Kinect considered by MS are highly, highly unlikely to happen in the future. All publishers are well aware that they have to provide the best possible 3rd party support ,quality and quanitity wise, so - in my opinion - next gen consoles will be very close to each other in RAW CPU,GPU etc power terms.

Long story short - consoles are like/will become more like a PC ( Personal Computer, open platform ) with closed ecosystem/services. 

4. Microsoft announced its plan to create X1-Windows10 ( Operating System used in PC, Xbox One )  common ecosystem, with games published on both platforms. The recent rumors about Forza 6, Gears of War series, Scalebound, Fable Legends, Halo MCC Collection PC versions shows this time Microsoft is serious in supporting Windows 10.

Long story short - Microsoft will create PC-X1 userbase to compete with PS4 and Nintendo NX userbase as a games publisher.

5. Brand loyalty literally do not exist in video games market - PS3, Wii U, Xbox One, Vita sales compared to its ancestors proves that. In my opinion, when  ne console is getting more value over another one, the userbase will swift big time. 

All of this, in my opinion, bring us to the point where the only factor, that can attract one console over another to the potential consumer are 1st party console exclusives. I dont see any other factor in the future that will provide advantage, if we talk about all-around video games console userbase.

And u ?

I guess if someone doesn't own an Xbox One or PS4, a big deciding factor would be which exclusive games they want more, since they're basically going to get the same 3rd party games anyway. But obviously there are other factors like platform features, what your friends own if they own anything (so you can play with them), and indie games.

But for Nintendo, their first party games have clearly been the biggest selling point of all of their consoles (and handhelds).

If the NX handheld can come close to XBone levels of power (or at least can play XBone-like games in power) it will have some 3rd party, just by the fact japanese companies will love to put their JRPGs console games o handhelds, plus the Vita will not have a succesor: handheld monopoly. Western games are the big question here.
The home console will depend on the nature of what on Earth the NX actually is and how does if functions.