A formal writing style is not necessarily “better” than an informal style, rather each style serves a different purpose and care should be taken in choosing which style to use in each case.
Writing for professional purposes is likely to require the formal style, although individual communications can use the informal style once you are familiar with the recipient.
Note that emails tend to lend themselves to a less formal style than paper-based communications, but you should still avoid the use of “text talk”.
If in doubt as to how formal your writing should be, it is usually better to err on the side of caution and be formal rather than informal.
State main points confidently and offer full support arguments. A formal writing style shows a limited range of emotions and avoids emotive punctuation such as exclamation points, ellipsis, etc., unless they are being cited from another source.