I'll agree with PhilUSAFRet - lots of variables. I have a Mele mahogany concert that sounds great now, in a high humidity Minnesota summer. When I got it in March it did not sound so good, even after humidifying and changing strings (LW). Same strings, higher relative humidity, and it sounds great. Can't wait until winter comes ... when the Mele may be in case prison. Oddly a different Mele I played before buying mine sounded wonderful in the dry winter air.
Strings can make a huge difference, and what sounds good on one instrument can sound bad on another. Experimentation is not that expensive, just budget for a new set of strings a month until you find what you like best.
So back to your original question - how much better will a $200 ukulele sound compared to a $100 instrument. You will need to decide that for your self. Visit as many stores as you can, play as many ukuleles as you can, and see if $200 is the threshold for your kind of "good" sound, or if it's $300, or if it's $150. I played a $150 Snail that sounded great (ebony) a few weeks ago. If I was looking for a new uke I would have bought it. For a laminate it had a good resonance and it played in tune. My Kala Traveler ($200) has an interesting sound, though not purely a ukulele sound to my ear (more a cross with a mandolin) with less body resonance. And my all laminate RipTide is pretty dead sounding compared to the rest, but there are no seasonal changes to the sound.
I hope these data points help. In the end it's your ear that will make the decision. Good luck!