"〜ちゃう" is often simply described as the casual/contracted/etc. form of
"〜てしまう", with no further explanation given. This would seem to imply that in
terms of meaning they are identical, with only politeness/formality
considerations determining which is used.

However, there is evidence that this is not the case. Although Google hits are
an extremely inexact measure, these are the rough figures for a few searches
(all in quotation marks):

  * 教えちゃいました = 60,000 hits
  * 教えてしまいました = 1,600,000 hits

  * 教えちゃってください = 28,000 hits

  * 教えてしまってください = **3 hits**

  * 食べちゃってください = 1,150,000 hits

  * 食べてしまってください = 1,800,000 hits

  * 報告しちゃってください = 1,150,000 hits

  * 報告してしまってください = **0 hits**

  * 感動しちゃってください = 600,000 hits

  * 感動してしまってください = **0 hits**

  * インストールしちゃってください = 230,000 hits

  * インストールしてしまってください = 645,000 hits

60k vs 1,600k is a big difference in relative terms, but even 60k hits implies
a perfectly acceptable form. However, hit counts of 0 and 3 are quite striking
and suggest that the forms are basically never used, even though the
equivalent 〜ちゃってください forms are.

So why exactly is it this? Why do some 〜てしまってください vs 〜ちゃってください pairs return
such lopsided hit counts, while others do not?

(Note: I'm looking for answers with a bit of rigor, ideally expressing a
general principle, and certainly going beyond "It just feels more natural for
some words" or similar.)

**Edit:** Couple of clarifications:

  1. The past tense (〜ました) example above is basically for context, I don't think it needs explication. I only noticed this phenomena with the 〜てください contexts. If it does or doesn't happen with other contexts, that would probably make up part of a good answer!

  2. The Google numbers are terrible, okay, point taken. It still looks to me like the possible number of hits for 〜てしまってください is either "virtually none" or "dozens to hundreds", with not much in between and no obvious relation to 〜ちゃってください numbers. If I've just chosen bad examples and there is actually a subtle gradient I'm just not seeing, proof of this would constitute a good answer. (In particular if anyone wants to search a proper corpus that would be great.)
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usage subsidiary-verbs
Usage differences between てしまう and ちゃう
I think that 〜てしまう in conjunction with past tense (e.g. 教えちゃいました/教えてしまいました)
puts focus on the sense of "regret" that this expression may convey. There is
no difference in how this meaning is conveyed with regard to formality,
especially when talking about something _you_ did.

As to why the formal version seems to be more common, maybe it’s because in a
situation where you revealed some information that you should have kept to
yourself, you’d better be polite about it ;)

On the other hand, with 〜てしまう plus imperative, the focal point would seem to
be on "finalization" of some action. I’d say that the easier an action is to
actually finalize (like 食べる, インストールする), the more likely you will be to find
examples of this construct.

However, 報告する should be possible to finalize as well. I think that one reason
why you got such results may be situational rather than grammatical. One
possible reason why the hit count for 報告してしまってください is zero might be my next
point:

Especially with informal Japanese, I think that 〜てしまう (or rather 〜しちゃう) plus
imperative may also convey sort of a "just do it" feeling (like 〜しちゃえば), which
may be a bad fit with formal circumstances.
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```

      (intesting about Google's hit-number inflation -- Hitgate)
    
```

もう感動しちゃってください etc. (I think) first appeared in a TV or print advertising copy.
It's very catchy and clever.

早速みんなに報告しちゃうよ！ -- This しちゃう suggests certain self-aware Narcissistic
personality (affected or exaggerated juvenility, immaturity) -- This is a
perfect match for the Internet-Facebook-SNS age and blogger persona.

このくらいで先生に報告しちゃうものなんですか？ -- a bit of 「テヘペロ」meaning.

So all forms of しちゃってください and しちゃう are used all over the net.

* * *

re: popularity of しちゃって

It could be that dialectical uses of しちゃって is contributing to obscuring
(generalizing) its meaning.

  * 博多弁: [ 勉強しちゃってん ] 「勉強してちょうだい」という意味です。ttps://nanapi.com/ja/51747   
  
‎

  * 広島弁 : ... ちなみに「○さんが ～された」は「～しよっちゃった」「～しちゃった」という表現を良く使います。oshiete.goo.ne.jp/qa/1703644.html ‎

* * *

"〜しちゃう" and "〜してしまう" can be similar, but often different.

1a. 感動してしまう -- didn't mean to / resisted it, but ...

1b. インスタで間違えて報告してしまいました -- did it by mistake / did it without intending to do
it

This can't be made into 感動してしまってください / 報告してしまってください

  2. 後でなんらかの嘘が ばれてしまうよりは、潔く報告してしまえば すぐに済む場合も多いものです。 -- do it and get over with it. <https://en.wiktionary.org/wiki/get_it_over_with>

For some reason, this doesn't combine with the ください (command) ending.

When giving such a suggestion, much more common is the 報告してしまえば ... form.
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I searched the word "shit" and got 417 million results.  
I searched the word "feces" and got 14 million results.  
"Shit" is a vulgar word and yet is much more popular than "feces" because
"shit" is an informal word and "feces" is a formal word.  
In casual everyday conversations, people will drop formality and use informal
words.  
That is why informal words and expressions are much more popular than formal
words.

That is why ちゃう is much more popular than てしまう.  
ちゃう is informal and てしまう is formal.
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