Global edition: http://gamrconnect.vgchartz.com/thread.php?id=230847&page=1

Shipments are measured in increments of 10k.

1 = 10k
10 = 100k
100 = 1M
1000 = 10M

Fiscal year format: FY3/1998 = Fiscal year ending last day of 3 (March), 1998

[1] This fiscal year is weird because Nintendo started ending the fiscal year in March rather than August. Therefore, this fiscal year is only seven months long.

[2] All shipment numbers for Sony after this point are estimates, because Sony unhelpfully stopped separating their shipment numbers by region in FY3/2008. I estimated by using VGChartz US data from the end of April for each year (I used April instead of March because having a month's worth of consoles on store shelves seems appropriate) and then I multiplied those US numbers by the ratio of NA/US from the lifetime sales chart.

Lifetime:
Nintendo - 318M total, 149M home consoles, 170M handhelds
Sony - 169M total, 144M home consoles, 24M handhelds

After PlayStation release:
OVERALL: 17 Nintendo wins (251M)
OVERALL: 5 Sony wins (169M)

HOME CONSOLE: 7 Nintendo wins (100M)
HOME CONSOLE: 15 Sony wins (144M)

HANDHELD: 13 Nintendo wins (153M)
HANDHELD: 0 Sony wins (24M)

After PSP release:
OVERALL: 9 Nintendo wins (161M)
OVERALL: 4 Sony wins (99M)

HOME CONSOLE: 5 Nintendo wins (61M)
HOME CONSOLE: 8 Sony wins (75M)

HANDHELD: 13 Nintendo wins (100M)
HANDHELD: 0 Sony wins (24M)

After PS4 release:
OVERALL: 1 Nintendo win (19M)
OVERALL: 3 Sony wins (25M)

HOME CONSOLE: 0 Nintendo wins (7M)
HOME CONSOLE: 4 Sony wins (23M)

HANDHELD: 4 Nintendo wins (13M)
HANDHELD: 0 Sony wins (1M)

* Sony's handheld + home console sales may not add up to overall sales because of rounding
** Nintendo's handheld + home console sales may not add up to overall sales because of Nintendo Switch

"Nintendo wins:
The rest of them"

It's comparing the amount of consoles they shipped in each fiscal year.

Yeah I know I didn't edit quite enough haha xD 

They've already suffered a huge decline. If anything, they're going to see growth in the next few years since the Switch is doing way better than the 3DS did in NA.

3DS shipments as of June 2011: 1.43 million (+110k in Q2)
Switch shipments as of June 2017: 1.95 million (+750k in Q2)

I clicked "Submit" and then I saw your edit. Oops.

But wouldn't this mean that in say 1987 the NES only sold 1.8 million? Because it says 100 = 1 mil I think I'm still confused ... lol 

Yeah, that's basically what it means. From September 1986 to August 1987, it shipped 1.8 million.

Ohhhhhhhhhhhhhhhhhh ...

this is only for North America ... 

*walks away in embarrassment*

With 3DS still doing decent and the Switch being a smash hit I think Nintendo will win but when 3DS sales start to drop even more Sony might have a chance to overtake Nintendo but I doubt it since the Switch will be newer.

So, out of 22 years, Nintendo won 17 of them? Pretty impressive. Should win this year again.