If a €15 straightener works fine for you and you're not having frizz problems, honestly you don't need to spend hundreds of euros. The real difference does exist but it depends a lot on your hair type and how particular you are about the final result. A cheap straightener heats and straightens, that's it. An expensive one probably does it more evenly, with less damage and keeps the result better over time, but that doesn't mean it's essential for everyone.
The thing is, premium brands like GHD or Dyson have better-thought-out technology: more even heat distribution, materials that damage less, features that actually make a difference. If your hair is curly, very damaged, or naturally frizzy, it'd probably thank you for it. But if you're already happy with the results and your hair is fine, it's just throwing money away. Your sister might see a difference because her hair is different from yours or because she's looking for a more polished finish.
My advice would be that if your Carrefour straightener ever breaks down, then yeah, consider moving up to something better quality. But until then, if nothing's bothering you, don't spend it. Some people invest in an expensive one and notice the change; some people spend €200 and wonder why they didn't do it sooner. It all depends on what hair you have.