Language prides itself on precision. It is a tough medium because language will never be able to fully recreate abstractions. For example, when we speak of "beauty" or "pain," different constructions and notions will cloud the mind. The symbolic nature of language helps to create this lexical ambiguity. Any time we can find precision in language, it should be noted.
The statement of "Today is Monday" makes more sense. The sentence clearly establishes the subject of the sentence. When finding the verb of the sentence ("is"), the subject becomes "Who or What 'is?" Thus, the idea of "Today" being the subject is clearly established. The use of "it" is not necessary. Therefore, clarity is achieved with "Today is Monday" as opposed to "Today, it is Monday."
"It" may be a personal pronoun or what is called a "dummy subject it" that substitutes for the actual subject of a sentence: "it" substitutes for "today." In fact, in both uses (personal pronoun and dummy it), "it" is used to substitute for the subject. For example, if we were talking about "Today" as a subject such as "Today is a bad day" or "Today is going to be a challenging day" or "Today is filled with appointments," then we could use "it" as substitute for "Today." The sentence "Today is Monday" is grammatically correct and clear. Saying "Today, it is Monday," employs both the actual subject ("Monday") and the dummy it subject substitute. Thus this structure is grammatically incorrect since duplication of the subject is not correct English grammar. For instance, in English, duplicating the subject by saying "The dog, it is fuzzy" is recognizably ungrammatical, and the same is true for the duplication of the subject in "Today, it is Monday." In short, "it" may not be used as a duplicate subject as in "Today, it is ..." but "it" may be used as a substitute, dummy, subject as in "It is Monday." For the purpose of correct grammar and syntax usage, it is correct to say, "Today is Monday" or "It is Monday" but never "Today, it is Monday" because it is never grammatical in English to use duplicate subjects: the subject "it" duplicates the subject "today."
Perhaps, the indecision on whether to say "Today is Monday" or "Today, it is Monday" derives from the fact that language undergoes changes from its linguistic history. For, the expression "Today, it is Monday" may have been the way to state which day it was in Old English, which was derived from the French of the Normans, the conquerors of England in 1066. Having slaughtered not only King Harold, but all the noble lords of England, William the Conqueror replaced the court with Normans and French became the official language of the court and of literature in England. (The tales of King Arthur are written in French). Therefore, to say, "Today is Monday," one said "Aujourd'hui, c'est lundi" which literally translates as "Today, it is Monday."
In the english language, "Today is Monday" is better.
Today is Monday.
Today is Monday is more likely to be used. Through linguistic changes over time it is allowable to leave out certain grammar parts and is still understood. In French they do the exact opposite. From English to French you may say, "I am eating bread." However in translating it to French it has to be specific where the translation would technically come out as, "I am eating some bread." It's the opposite effect here with English. You don't need to indication that the IT part is referring to Monday. You can just say "Today is Monday" so as not to necessarily repeat yourself by saying today, it is Monday. You can use either but it will more commonly be "Today is Monday."
From me, I believe you draw from daily life speech---"It's Monday!" and you normally do not say "Today, it's Monday!" as it is grammatically wrong in terms of syntax. The word 'it' itself is suppose to replace the actual noun that you are planning to use. If you insist on using this fixed set of words, the better way would actually be "Today-it's Monday!" . The break-off midway into the sentence allows for the usage of it. But in terms of common or daily usage, people more or less say "it's Monday" so it is uncommon and unusual to use "Today-it's Monday".
In the English Language it is better to say "Today is Monday".
Today is Monday.
Personally, I think "Today it's Monday" is the appropiate way of saying it in these modern times. Most of our spoken language is filled with conjungtions. "Today is Monday" is not correct, "Today it is Monday" is correct, but in these modern times, "Today it's Monday" is more commonly used.