As a comparison to functionality compared to Desktop, in my storied opinion based on over 20 years using desktop, the closest thing today to Desktop Pro (the least expensive desktop version) is now QBO Advanced, since they implemented user limits on certain functions in the other 3 full online versions. Cost of Advanced for the promo 3 months half price will actually exceed street price of Desktop Pro at Staples, Costco, Amazon. If you are only one user and do not need ability to have an app on your phone then desktop on a PC is your best bet.
As far as desktop versions, it depends on your needs. Pro and Premier are the same exact product but Premier adds a few bells and whistles. A Pro company can be opened by Premier and vice versa. Enterprise is more powerful but is a separate database underpinning it and it takes professional paid help to convert back
QBSE (self-employed) is the odd one, geared to sole workers, more for the gig economy but even then a professional musician or one with a musical side-hustle would find it constraining in that you cannot change the chart of accounts or track depreciable assets (a $3500 Gibson is a depreciable asset)