Articles on the internet say user-defined functions can either burden or increase the performance.
Now, I know that standard SQL is pretty limited, however, some of the behavior can still be written as in T-SQL built-in functions.
For example, adddays() vs. dateadd() . Another point I've heard that its also better to use coalesce() - the ANSI standard function rather than isNull().
What is the performance difference between using the ANSI SQL standard functions vs T-SQL functions?
Does T-SQL adds any burden what so ever on the performance with it trying to make the job easier, or not?
My research does not seem to indicate a trend.
You will need to approach this on a case-by-case basis and do actual testing. There is no general rule, other than Microsoft tries to make the entire stack perform as well as possible. TESTING is what you need to do - we can't tell you that always a certain thing would be faster. That would be really bad advice.
It is important to do this testing on your actual production data, prefereably a copy of it. Do not rely on tests done against data sets that aren't yours. When you're talking about performance differences of functions, some very subtle things can make a big difference. Things like the size of the table, the data types involved, the indexing, and SQL Server versions, can change the result of these tests. That is why "no one has done this" for you. We can't.