Why Use the new syntax?
As others have stated, the new syntax has become the preferred convention. In larger queries the new syntax is easier to read, debug, and ensure the join criteria is added (meaning no accidental CROSS JOINS
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Is the old syntax deprecated (for inner joins)?
Not according to ANSI -- both are valid, even if the first is disfavored. Although, performing outer joins in the old syntax has been deprecated -- mainly because it can be ambiguous.
How consensus is the "use the new syntax" view ?
- Aaron Bertran considers it a "bad habit to kick"
- SQL Server Central the consensus was "Kill kill kill it with fire"
- Joe Celko -- meh, but it's easier to read.