Why do touch ups on flat paint show?
At minimum, you have to let the paint cure before you can really compare it.  It will blend in over time for the reasons bib mentioned.

It might also help to wipe down your walls - smoking, cooking, dirt and grime will discolor them, sometimes noticeably.

Find out how the new paint was applied.  If the original paint was applied with a roller, and the patch with a brush, there will always be a noticeable texture difference.

If the patch was not primed before it was painted then this might cause a color difference too.

Really the only way to get a perfectly blended wall is the repaint it.