Inserting to table: Insert rows with Left Outer Join or Insert rows then Update?
When Orders and Deliveries are both properly indexed, the second query will generally perform better. There are two main considerations here:

Generally speaking, and without seeing the details of your tables - what probably happens with the INSERT/UPDATE construct is that it will first allocate a number of pages in the database in the initial INSERT. But when you UPDATE those records, the added new information has to fit inside those existing rows in the OrderInformation table's pages, which causes page splits, which are very I/O intensive and can fragment your table and/or indexes.

The second query (single INSERT using LEFT JOIN) is considerably better practice, since it minimizes the locking requirements. Imagine if another simultaneous process creates a new row in Orders and then a related row in Deliveries between the time of the INSERT and the UPDATE statements in the first example - you'll get a foreign key constraint violation unless you've put all of this in a potentially large transaction, which itself implies a bit of overhead.