If you're shooting with a tripod ­— a good, solid one, not a sub-$100 deal — image stabilization isn't very important. If you're shooting in a controlled environment with strobes, it's not very important either. Or, if you're shooting in very bright light where you can get good depth of field and a fast shutter speed (to today's standards of pickiness, much faster than ¹⁄focal length), not important.

But, for focal lengths over 100mm, if you're hand-holding, if you can't get to very fast shutter speeds, you'll need optical image stabilization to get sharp results. So, the question reduces to: are you shooting in those situations, and are sharp results important to you?

That last question part is somewhat mind-blowing because if you read camera forums you often encounter an almost religious focus on sharpness as the measure of success of a camera, lens, camera system, photograph, or photographer. That's... a fine cult, I guess, but isn't really the only way to go. There are plenty of other schools of thought on the matter. If you're willing to relax on that a little bit, you might be happier saving a bit of money.

Note that both of these lenses are super-budget lenses, a zoom and a "superzoom". They're amazing for what they are, but they have a lot of compromises in order to get to that price point with that zoom range. Stabilization will not change that — and in fact the lens with stabilization is also the one with greater zoom range, and in order to get that all in at that price point, there's likely (and reviews bear this out) even more compromise around distortion, sharpness, and aberrations. So... really it comes down to which compromises are more important to you.

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In a comment, you add:

I have an EOS 450D (that I basically only use with the cheap Canon 50mm prime lens to do portraits of my wife and son). I currently live in NYC in an apartment with a nice skyline view so I'd like to take pictures of e.g. Manhattan at dusk, etc. So I guess [...] I'm looking to optimize the quality of the long range shots I can take, while also being happy if for about the same price I get a more versatile lens.

... and in this specific situation, we can give specific advice. Particularly, presumably you have room to set up in your apartment or on your balcony. Get a tripod (see this Q&A for advice — budget around $200) and don't worry about image stabilization. You'll probably want to be working at f/8 (on whatever lens you get), and if you're looking to shoot at dusk, you don't have good light, so you'll need long shutter speeds.

Reviews of the Sigma 18-250 indicate that its OIS is good for three stops, so if we assume ¹⁄₄₀₀th as a rule of thumb requirement for handholding, that'll buy you down to ¹⁄₅₀th (one stop faster: ¹⁄₂₀₀th, two stops faster: ¹⁄₁₀₀th...). That's not going to be fast enough at dusk even wide open at f/6.3, so you'll want a tripod anyway.