The title says it all. My favorites are the Muhle R41 on a short, fat handle and the Rockwell 6C with the #4 plate. I haven't tried the #5 and #6 plates yet. The Rockwell w/ the #4 plate and s 7 o'clock super stainless is a mighty sweet shave.
Gillette slim & second place would be the Razorock Wunderbar & Schick SE Canadian E5 black handle with a chick blade(Very rare aggressive beast). The nice thing with a adjustable you can dial in your shave to your likening.
Weber PH with Classic handle Any Gillette Adjustable, Fatboy, Slim, BB Parker Variant Gem Micromatic OC
Blackland Dart Rex Ambassador(6.5) Above the Tie H2 Schick E2 (early version that opens for cleaning) Pal Injectomatic Ever-Ready 1924 Fatip OC Gillette Fatboy (9) Out of this lineup the Dart has the most blade feel and the Rex is the smoothest.
@Pete123 -You didn't specify modern or vintage so I'll split my choices. Vintage; Early Gillette #195 Red Tip New Long Comb Modern; Fatip Piccolo Futur clone (Ming Shi 2000s)
Until recently I'd never tried an Old Type, but they do offer a very smooth shave. New LC is a beauty to shave with too. And I can't ignore my Aristocrat #15. It's so pretty.
I'm going to have to give adjustable razors another try. I bought a vintage Gillette and it was defective and I never circled back around to try another.
No overcoming a defective tool. If you still have it one of our Vintage Gurus may have tips to correct the problem. That's been my experience. Part of Mildness is a reduced effective shaving range because the blade is less exposed. Opening up an Adjustable gets the blade out there where it can get the job done. Riding the Cap has made for less nicks in my experience.
I don't submit myself to really aggressive razors anymore, but when I did my favorite was the Icon Shavecraft Tech. Very aggressive, very smooth.
No particular order: PAA DOC EVO SS Ikon Tech Gillette Single Ring Dart Otto Kampfe Modern DE Merkur Vision R41 Parker Variant Gillette Old Type Rex Ambassador
R41 was for a long time my favorite razor. Since then I have been developing enough skill to be able to use ultra mild razors (they requires a more precise angle or they will not shave close). Now my favorite razors are iKon X3 and Saiver travelers razor (loaded with included blade separator and only one blade). I also have the mild Mamba, which I consider as a top razor although I do not shave often with it.