Stainless steel is iron with at least 10.5 % chromium; the chromium oxide film is what makes it stainless. A nickel alloy is nickel-based, usually well above 50 % nickel, and it keeps its strength and corrosion resistance where an iron-based alloy gives up: above roughly 600 °C, or in chlorides and reducing acids.
The base metal decides almost everything
Stainless steel is an iron alloy. Chromium at 10.5 % or more forms a passive oxide film a few atoms thick, and that film is the whole point: it re-forms when scratched, which is why the material stays bright and does not rust like carbon steel.
A nickel alloy is the other way round. Nickel is the principal element, and chromium, molybdenum, cobalt, niobium and aluminium are added to it. Nothing about the structure depends on an iron matrix, so the alloy designer is free to put in far more of the expensive elements than an iron matrix would tolerate.
Where the difference actually shows up
Chloride stress corrosion cracking. Common austenitic stainless grades crack in hot chloride service, sometimes within months; the higher-nickel alloys resist it. This single failure mode sends more stainless parts to the nickel-alloy shelf than any other.
Temperature. Above roughly 600 °C an iron-based austenitic loses creep strength quickly. Nickel-based grades hold theirs to 700-1000 °C depending on how they are hardened.
Reducing acids. Hydrochloric and sulphuric acid attack the oxide film that protects stainless steel. Molybdenum-bearing nickel alloys such as C-276 and B3 are built for exactly that chemistry.
It is not a ranking, it is a fit
A 316L tube handling clean cooling water is the right answer, not a compromise. Putting a nickel alloy there buys nothing and costs several times as much per kilogram, because the nickel, molybdenum and cobalt in it trade at multiples of the iron and chromium in stainless.
The practical rule: start from stainless, and move up only when you can name the mechanism that defeats it — cracking, oxidation, acid attack or creep. If you cannot name the mechanism, the problem is usually the grade selection inside stainless, not the family.