The most essential function of a scope is that it works in a way that makes you trust it. Ok some of the scopes here have limitations such as 100MHz BW, that has nothing to do with trust, if you suspect a VERY narrow noise pulse and do not see it you get a better scope off the shelf.

BUT I have worked with scopes that would sometimes miss a trigger (i.e. tell me there was nothing there when in fact there was), and in my opinion, I would rather be without a scope than use such an instrument. If a scope does not faithfully do what you expect it to do, you are worse off than if you do not have a scope.

So if the result is not a 100% trustworthy instrument it irrelevant if it is "Cheap", "Hand Held", "Digital" or anything else

Erik