This is a fun topic as the options are endless. I have just started playing around with pressure ferments and the results are striking. So far, I would say pressure fermenting takes away some undesirable flavors for any style and makes beers more "commercial" tasting. When I say commercial I mean finished, clean or less flabby compared to general homebrew. This is a general positive but for some ale styles, flavors can be mutes for esters. That is a broad brush but the ales I have done with higher pressure (1-2 bar) have a more muted ester profile.
The biggest thing for me is the hop profile is massively different than non pressure ferments. Dry hopping, bitterness and overall hop flavor is much more present when using higher pressure. I made an IPA that started with 2 bar and kept it all the way through and the end result was like - "that is why commercial IPAs taste that way...". The big breweries are forced to deal with pressure as their large fermenters create it naturally.
So the levers I see for brewing with pressure and making different styles are:
1) Temperature - raise it higher than you would without pressure if you want to reclaim some esters. Stay low for lagers for better than normal lagers. No need to ferment lagers higher just because everybody is doing it. But pitch plenty of yeast.
2) Amount of Pressure - Higher is cleaner (fewer negative flavors) with more hop presence. Lower is more esters and less captured aroma.
3) When the Pressure is Applied - Starting at a higher pressure from the get go is replicating a commercial fermentation. This will result in the most pressure affected flavor outcome. Pitch your yeast and hook up a CO2 tank and run the pressure up. Super clean and hoppy. On the flip side, let the ferment start without any pressure and close the spunding valve down once you pass 50% attenuation and add your pressure profile. All ending at carbonation spunding levels in the end. This will capture some aroma goodness while letting the yeast express itself (like that term!) early in the ferment when flavors are usually formed.
What is odd to me is that yeast give off flavors when they are stressed and pressure stresses yeast. Yet pressure fermented beers are cleaner with lower off flavors. A mystery.