If you have your technique down right the Fatip Piccolo & the Grande are very smooth shavers.
My Piccolo Special Edition has a 19mm cap. Fatip tolerances, as good as they are, can be "special".I cant speak to Parker razors as I've not used one.
The Mk.1 Fatip cap is 18mm wide. The Mk.2 cap is 19mm wide and the new Piccolo Special Edition seems to have a cap width of 19.6mm.
I wouldnt call my Mk.2 Grande aggressive at all, it is however incredibly smooth. My R41 is aggressive and not what I'd call smooth, yet the both have similar blade exposure.
I'm really not sure any other DE could be compared to a Fatip, none I've used could be. I've never used a smoother more efficient DE. Mine can go from being as mild as a post war Tech to being nearly as efficient as my MMOC, all in the space of a ~10° change in handle angle and adjusting pressure.
If you want something a little more user friendly than a Fatip OC, try a Gentile. The Schone is another alternative and its said to be quite mild and forgiving while still being efficient. All are solid Brass.
As Ron said above, its all in the technique and how you use them. As shallow as I use my Grande, its as mild as my post war Tech and 5 times as efficient. Its all in the angle of use and pressure applied.
I gave another try to my Piccolo (a special edition with 19.6mm cap) this morning and, while smooth, it's extremely efficient and I ended with some blood on the neck at a few places.
This is way too much for me.
The Testina Gentile is less agressive.