The different usage between "致します" and "申し上げます" interms of 補助動詞

Question

As titled, I have difficulty telling when to use "致します" or "申し上げます" as opposed to the other one. For example,

ご連絡くださいますようお願い致します/お願い申し上げます。

ご愛顧を賜わりますようお願い致します/お願い申し上げます。

here is another one

お待たせを申し上げまして、大変に失礼をいたしました.

お待たせをいたしまして、大変に失礼を申し上げました。

Answer 1

申し上げる is the 謙譲語 form of 言う (say/state). お礼を言う、お願いを言う。It is also used in the sense of ‘to do something’ (in a positive way) for someone who is respected or above the speaker in station.

致す is the 謙譲語 form of する (do). お待たせする、失礼する。

These are different words, albeit with occasional similarities and overlap in use and in nuance.

In many cases, 申し上げる is an even more polite form of 致す.

The main difference would be that using 申し上げる implies that you are doing/have done/will do something positive, whereas 致す is more neutral and can be used for expressions showing both positive and negative actions.

If you think of it this way, your example: お待たせを申し上げまして doesn't make sense, as making someone wait is not a good thing.

お待たせを申し上げまして、大変に失礼をいたしました。

お待たせをいたしまして、大変に失礼を申し上げました。

These sentences are not the best examples.

First, using the particle に after 大変 is, in this case, not grammatically correct. In this usage, it is a nominal adjective. In the expression 大変になる, on the other hand, 大変 is functioning as a noun with a different meaning and conjugation.

Second, お待たせいたしまして (make someone wait) is the set expression. お待たせ申し上げまして ('make you wait') is stating something regrettable (negative) that was done and is not used.

Third, I assume that you are aiming for an apologetic expression. お待たせする and 失礼する are both explaining what was done to necessitate an apology. They are the lead-ins. 'I was rude for making you wait' is not a valid apology and this combination would not be used in Japanese. Either 'Sorry for being rude' or 'Sorry for keeping you waiting' are more appropriate, as shown in the examples below.

お待たせいたしまして、お詫び申し上げます。

お待たせいたしまして、申し訳ございませんでした。