So again, what exactly did they change and would it be worth for me to try the game again after I failed so many times in the first world?
Have you made it to World 2? If not, then yes try the game again. Otherwise I'd say it's up to you.
...means it goes back to non-dumbed-down (original) level design after your first full playthrough?
The signs are tacky as shit, but do not affect the level design. Given the broken, yet consistent, jumping mechanics guess it's helpful the first time through. There used to be spikes instead of the drop where you can come back around. Honestly, I'm not sure how useful a change that even is. I'm sure I've fallen on those spikes in the past, but they only cause 1 damage. It's not like they automatically kill you. It's obvious you need to double-jump to make it across. The jump itself is the same.
Those are the only changes. All enemies are in the same position. I had killed the bee/wasp before taking the screenshot.