TBH, I don't think the photos were ever going to be that much more groundbreaking to your average person, given the fact that the angular resolution of the telescope is roughly equivalent to the Hubble.
It's got a much bigger mirror, so why is this the case? Well, it's because the Webb works primarily in the longer, infrared part of the spectrum, not the visible. Resolution is related to the diameter of the mirror and the wavelength being studied - the longer the wavelength, the bigger the mirror you need to achieve the same sharpness.
But working in the infrared part of the spectrum means that Webb can look further back into the past, because the oldest light created by the earliest galaxies has redshifted out of the visible spectrum because of the expansion of the universe. So we'll be able to collect and see much older light from much younger galaxies with Webb that Hubble literally cannot detect because of this redshift.
On top of this, infrared, being a longer wavelength than visible light, allows us to see through dust clouds more readily. Notice how many more stars are visible in the Carina Nebula comparison.
Lastly, the Webb has other instruments such as a spectrograph that allows us to determine the chemical composition of distant objects (such as planets). We can point it at an exoplanet and determine, say, if it has water in its atmosphere.
In total, it means marginally better photos for the general public, but a great deal of new data for scientists that should greatly further our understanding of the universe.