Yeah, mini systems and boomboxes seem to have retired the EQ for the preset sound settings "rock", "jazz" etc.

I am not up on mini systems. Depending on your budget you might take a look at the NAD CD/receivers. They are under $500.00 and paired with a decent bookshelf you'd have excellent sound quality. Of course, no EQ, but resolution beyond what you are currently used to. Unless used a decent bookshelf will set you back at least $200.00 give or take though. NAD makes these receivers with built in CD player so it's one box.

Another suggestion, if room isn't a factor and you have Craigslist in your area you can usually pick up an older receiver and an actual EQ for little of nothing. You have to watch though, some people try to sell those vintage receivers for way more than they are worth. You should be able to get a working receiver for under $100.00 and an EQ for under $50.00, way under usually. Take it old school for great sound on the cheap. You can also browse thrift stores. I once bought a Sansui integrated for $20.00 to later find it was a sought after collector item. When I listened to it I could understand why.

Sorry, I didn't answer your original question but if your goal is sound quality you might find these options useful If space is limited and you really need a mini system the two brands you are looking at are respectable and would be at the top of my list in mass market brands.