Attn: Not for the faint of heart! hehehe...
Well, I've been thinking about this thread for a number of hours now, I've done some field work, conducted a bit of research, talked to people, and even taken a few blood samples, and here are my conclusions (some of which have already been mentioned here):
I very much agree that "
would" is used more in narrative than "
used to," but
not because of any difference in formality; rather, the difference in usage is based both on
syntactic as well as
semantic differences between the two. That being said, however, there may in fact be a
perceived difference in formality between the two, based primarily on the greater usage of "
would" in narrative than of "
used to" (thus leading "
would" to
seem more formal).
The principal differences between "
would" and "
used to" are twofold but not completely separable. First of all, they are used in
syntactically different situations. "
Would" (as mentioned above by giovannino) almost always requires some subordinate clause or a previous sentence acting in that same (subordinate) capacity, or at the very least an adverb, in order to give the verb a more explicit habitual denotation; "
used to," on the other hand, does not need any other syntactic padding than the basic parts of a simple sentence (subject, verb, object):
(1a)
I would go to the movies. 
(1b)
I used to go to the movies.
In (1a) there is not enough information in the sentence to give "would" a more explicit habitual denotation; in (1b), however, "used to" does not require more information.
(2a)
I would go to the movies every day.
(2b)
I used to go to the movies every day.
(3a)
When I was a kid, I would go to the movies.
(3b)
When I was a kid, I used to go to the movies.
(4a)
When I was a kid, I would go to the movies every day.
(4b)
When I was a kid, I used to go to the movies every day.
In (2a) and in (3a) I have added extra information, but it does still not help the sentence with "would"; it still sounds unnatural because there is not enough emphasis on the habit of the past action. (2a) begs the question "When?" and (3a) begs the question "How often?" Again, however, (2b) and (3b) with "used to" are perfectly fine. "When" and "How often" are of no concern because "used to" emphasizes both past tense and habit by itself. But combining (2a) and (3a) to get (4a) finally becomes satisfactory, so that the sentence provides an idea of "when" and "how often."
Before moving on, some might ask, "Well how/why does '
used to' answer the questions 'when' and 'how often,' but '
would' does not?" My answer: Without having more context (i.e. in a simple sentence like (1b)), "
used to" refers either to a
state (as mentioned above by giovannino) or to a
non-habitual action! "I used to have long hair" refers to my past
state of having long hair; "I would have long hair"
cannot work. In (1b), "I used to go to the movies" refers to my
non-habitual action of going to the movies--i.e., I simply went to the movies every now and then but not on any regular basis; it was an action in which I engaged at times but not habitually--"I would go to the movies"
cannot work. However, adding more context, like "When I was a kid" and "every day,"
forces "used to" to become
habitual, just like "would."
As a last point on syntax, both subordinate clauses and adverbs
tend to precede "
would" in a sentence, while "
used to"
tends to precede its sentence's subordinate clauses and adverbs. Compare: "
Every morning at 6 am, he
would wake up and go for a run" vs. "He
used to wake up
every morning at 6 am and go for a run." To me, "Every morning at 6 am, he used to..." sounds
very awkward. If you'd like more information on this part of the syntactical differences, please PM me.
Now, syntax aside, the second principal difference is
semantic (i.e. the words carry different connotations). As mentioned above by Cappers, there is an issue of time reference here: "
used to" always makes some (possibly underlying) comparison to the present tense, while "
would" is more general and concentrates on the past. "
Used to" implies quite directly that, for whatever reason, the action no longer occurs during the present time or, at the very least, makes the reader/listener wonder, "Does he/she still do that?" "
Would," on the other hand, simply states the fact of the habitual action and does not say whether the person still continues it to this day. The best way to see this is in narrative (forgive me for my terrible prose!):
Jack Hilbert was a very unusual man, even for one who lived in Rogers Park in the '60s. He was always up late at night wandering the streets and smoking Camels and picking up the stench of old Chicago. He used to wake up at 6 am every morning with that same stench and revel in the fact that he could start all over...
This use of "used to" makes me immediately ask myself, "Did he stop doing this? Why? Will I find out later?" He probably did in fact stop that habitual action; otherwise, the sentence would better be written as "He would wake up at 6 am" or "He always woke up at 6 am," neither of which imply or deny that he continues to do so to this day. Consider (1b) above: this implies that I no longer go to the movies at all. (2b), however, implies that I no longer go to the movies every day (but perhaps I still go occasionally).
Sometimes the reason for the character no longer doing that action could be as simple as death. Sometimes it could be more important, such as a change in lifestyle or some crucial plot twist. In any case, "used to" implies that the character no longer does that action.
Some final remarks. I would hypothesize that the predominance of "would" over "used to" in narrative, and similarly of "used to" over "would" in spoken language, is not due to any sense of formality, but rather to a number of factors. In a narrative the author usually describes basic (habitual) actions that the character may or may not continue to do during the present time. Often, it is not important whether the character does not continue to do them, so it is of no use to confusingly use "used to," which makes the reader infer that the action no longer continues (and is therefore of some importance); and if the action does still occur, then the author cannot use "used to." Furthermore, given the right context and syntactical features (as mentioned above), "would" can do the exact same job as "used to," so that by using "used to" once and then using "would" a few times, the author can avoid cumbersome repetition.
The reason that "used to" is more common than "would" in speech is because most people describe past habitual actions that they no longer do; if it were my intention to explain a past action that I still do, I would simply say "I have been doing ____ since..." Moreover, as seen above, "would" requires more words and contexts, so it's simply shorter and more convenient in conversation to use "used to."
Thus, I see no real formality issue between "would" and "used to"; the differences to me are purely syntactic and semantic. If anyone does feel there is a difference in formality, I would say that it's precisely because "would" is used less in speech and more in writing/narrative.
