If your main concern is efficiency of storing and retrieving data, I'd recommend adding a new
sparse column in the existing table. However, if you are dealing with OLTP system, you may have good reasons to choose new table with 1-0..1 relationship.
For instance, there are many legacy applications using existing model which potentially may be broken because of new column. Also, if a new column is any blob,
select * in legacy application (despite the fact it's not a very good practice, such queries are quite common) will affect performance.
Secondly, new column may be accessed with different pattern (say, you mostly read old columns, but perform many updates of new column).
Also, I saw many tables which used to be more or less normalized in the beginning, but ended up with hundreds of columns ; some of the columns were not used anymore, others don't fit the model (it's even better to say the model was destroyed). This note is probably out of the question scope, but in my opinion worth mentioning...