Oops, I'm sorry that's a typo, I meant GBS-C.
The difference between the OSSC and the GBS-C are quite a few and those differences are kinda key depending on your uses.
The main thing going for the GBS-C is, from what I can read as I don't have one, that it can avoid the flicker from unfiltered interlaced video modes by using adaptive deinterlacing.
I don't know how knowledgeable are you about this stuff but I'll explain on simple terms: you have "three" general video modes when dealing with older stuff. Those are 240p, 480i and 480p.
Of those, only 480i is interlaced. Interlaced means that only half of the horizontal lines gets updated at a time. This causes the screen to feel "jumpy", specially with white or close to white colors". This is what the majority of the PS2 games have, because the games have very, very poor support for Progressive Scan (480p), and few games use a filter to masquerade the shifting picture with each refresh.
Generally speaking, modern TVs have a filter of their own if they find an Interlaced signal that blurs the picture, but at least protects your eyes from the flicker. But if the picture is passed through an upscaler that changes the image, that filter might not be used at all. Most systems (Dreamcast, Gamecube, Xbox, Wii) did also apply a filter to hide the flickering as it can strain your eyes because, after all, you are looking at constantly shifting lines of bright light. But as mentioned, Sony for some insane reason thought providing a filter wasn't good.
The GBS-C has a feature that can provide both a sharper picture and avoid the flickering. As mentioned, this is good for most PS2 games, and some PS1 games that play at 480i. It can also help with games that change from 240p to 480i, mostly PS1 games although not many do it.
The OSSC still can do something called BoB Deinterlacing. it offers a cleaner picture but you can still see the flickering a bit. You can use scanline options to hide it pretty well, but it's not as good as the feature of the GBS-C. You can still just "pass through" the video signal and let the TV use its own filter, you get usually a cleaner image than directly plugging your system to the TV, but it's not as good as if you upscaled it of course.
On the other hand, the OSSC- is superior in most other areas, and it's better with 240p, which is most of the PS1 games and some PS2, and 480p, which is pretty much all the Wii and GC stuff (if you play with Progressive Scan forced), plus you could use the Wii's awesome 240p support for emulation and upscaling it over what a Wii U could offer.
Or, to summing it up, if you really want an upscaler, you have to either choose to give priority to the PS2 or the Wii.
I guess one option would be to get a GBS-C for your PS2 and connect the Wii to the TV through component directly. It'd be cheaper and the PS2 needs more help because of the Interlaced video mode.
Personally I give far more importance to the Wii as it offers me better picture quality for more systems to play (counting Wii, GC and all the emulation) while also giving more time to PS1 than PS2 games, so the OSSC fits better my needs. And I'm still fine with the PS2, with some scanline configuration often I don't even notice the interlaced flicker and I play on a desktop and close to the TV.
It can get pretty annoying to decide what to do because answers aren't simple, so I'm sorry I can't simply say "do this".
JM 
