'Deeper blacks' is a term I often hear, but it's never quite clear to me what people mean by it.
Technically speaking, in the digital realm, black = RGB 0,0,0. It doesn't matter how an image is acquired, it's always possible to set the black point to that absolute black. Scanners do not differentiate in this regard.
So with that out of the way, I can imagine that 'deeper blacks' refers to either (1) differentiation in the shadow areas or (2) the exact opposite; i.e. allowing large part of the image sink into absolute black. Either of these are determined by curve adjustments that are applied to scans. Again, scanners do not meaningfully differ in this regard; any scanner out there will be easily capable of picking up even subtle gradations in the lighter parts of a B&W negative, i.e. the deep shadows in the final image.
Hence, I think we need to set aside the issue of the 'deeper blacks' as one that mostly relates to post processing and has no bearing on the choice of a scanner. It is conceivable that the 'out of the box' curve adjustments you got from your commercially-made PII scans were pleasing to your eye; I don't contest that, but it's more a matter of competence and taste in post processing than a clear determinant in choosing between scanners (of any type).
As to fine detail: the Precision II will outresolve the Minolta on 35mm (evidently other formats are beyond scope of that particular comparison), but I personally find the relevance is only there if you end up enlarging the image substantially - think of prints larger than 30x40cm. At that point, differences will start to become apparent, but in all frankness, if your photography relies heavily on very fine detail rendering, I doubt you're enlarging 35mm that far as the format is just insufficient for really crisp detail rendering at such enlargements. However, there is a real difference between the Precision II's 5000 dpi (ca.) and the Minolta's 2800dpi. The difference IMO is only relevant if you look at finer-grained, high-resolving films in the 100-speed range (or slower) and fine-grained faster films like Delta or TMAX400. For coarser grained films like Double X, HP5+ etc. I personally see very limited/marginal advantage in scanning at full resolution on the Precision II vs. the Minolta. The speed difference of course is very real, so I virtually always use the Minolta as it's a heck of a lot faster.
For medium format I can only say so much as I don't have hands-on experience with the 120 format scanner you use. I understand it effectively resolves around 3000dpi and that's about what the PII will also give you on medium format (unless you resort to strip-scanning as if it's 35mm and then stitching back together). Also here I doubt the resolution difference is all that relevant, but there will again likely be a marginal benefit for the PII.
The PII does come with a couple of caveats like you know; it practically works best on older hardware, which means you generally end up having to dedicate a separate machine to run it, which takes up space. It's also a very slow scanner, and while they are very robust, there's always the odds of defects on the 25+-year old hardware and it will have to be seen if those defects are repairable if/when they occur (of course, this is also true for your Minolta).
If you're presently looking to set up an alternative way of scanning your medium format and 35mm film and you're looking at a technically high-performing approach, I really doubt if I would recommend something like the PII. I'd sooner lean towards some form of camera scanning, even though a high-performance setup may end up costing significantly more than the €700 base price for the PII that you've been offered (depending on what kind of digital cameras and lenses you may already own).