I would definitely say, however, that Peter Parker is the stronger persona over Spider-Man.  He is who he is due to his humanity rather than his powers.

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Originally, Spider-Man was the ultimate wish-fulfillment character. Whereas Clark Kent, during the same period, was an "act" and Superman the "real" character, Spider-Man was in many ways an "act," and Peter Parker who he really was. Spider-Man was the "rock star persona" -- Peter's id unrestrained. Peter would always be too polite to refer to Jameson as "old Flat-Top" but Spider-Man easily would.

This is why it always seemed "off" to refer to Spider-Man and Peter interchangeably. Just as I don't like how in modern comics, Peter pretty much behaves like Spider-Man even when out of costume. In the Lee/Ditko classics, Peter was much more morose and glum than the cocky Spider-Man -- and even when Spider-Man was, while in costume, brooding, it was in Peter's internal monologue.

There are a few cases where I'm more likely to refer to, or think of characters by their civilian names. These include the FF members, since it just seems natural for me to think of them as Ben, Reed, etc. Also, Spider-Man gets thought of as Peter sometimes, but not always, possibly because I identified with him so much as a youngster.

   I tend to think of GLs as Hal, or Guy or Alan, but that's just for easier differentiation.

   The X-Men seem to go either way, sometimes by code names, other times by civilian names. I might say "Cyclops" but I never say "Cyclops and Marvel Girl" but rather "Scott and Jean"

    Superman is always Superman, Batman is always Batman.

     Captain America is certainly always Captain America.  

Overall, the characters I like the most, I call them regularly by their first names. Clark, Bruce, Hal, etc. Or at least, interchangeably.

The ones I don't, I call them strictly by their superhero names, or last names, if applicable. Spider-Man, Hulk, Richards, etc.

The only exception is Captain America, who is a character I really like and almost never refer to him as Steve. He's mostly Cap to me.

Joey da Q once said in an interview that most Marvel characters are the civilian identity first and foremost, with an alter ego. 

As far as names, I agree with this for the most part...Wolverine, Mr. Fantastic, the Thing, and Spider-man are very easy to call "Logan", "Reed", "Ben", and "Peter". By contrast, Wonder Woman does not summon up "Diana" very easily, I call the Flash 'the Flash', and Superman and Batman seem to be very clearly delineated namesakes depending on whether they have the costume on, or not. 

At least in the case of Batman, I would say that Bruce Wayne is a disguise. I believe it was "Arkham Asylum" where the criminals were about to unmask him, saying "I want to see his real face"--to which the Joker aptly replied, "That is his real face, you moron!" Good scene. :-)

Stan encouraged the personalization of the letter columns, with "Dear Stan and Jack" or "Dear Stan and Steve" instead of DC's colder and more distant "Dear Editor", and with this I think he may have accidentally opened the door for a similar way of thinking about the characters. So the native awe that had been so important to the superhero mythos began to slowly erode, and where we sit today was the long result.