It all depends on what you determine is better. Are you looking from a value stand point? If so, a stamp on paper with the entire envelope likely has more value, but not always. Check the catalog to be sure.
Are you looking for specific collecting purposes? I nearly always take the same off paper because I collect singles. Having the entire envelope takes up a lot more space when you are collecting 1000s of stamps.
I am sure there are other ways to define better too. What are you looking for?
I generally remove them unless there is a significance to the cancellation, the cancel date, design on the envelope or the sender/addressee are of some historical significance. Date of first issue, or date some how related to the subject on the stamp, a pictorial cancel related to the subject... etc.
For older issues (1800s), if on a complete envelope and it's in relatively good condition for its age, I'll usually leave it alone.
Some envelope paper is not "archival" and could harm stamps over the years. Plus, envelope paper is often much thicker than the stamp, so will take more shelf space. Dan
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