Recursive parsing of CFGs is only better when they're LL grammars, but LR grammars (which are the most common grammar used in programming languages) are definitely better with an explicit stack due to the repeated way the state machine needs to run. You might be able to do a nicer LALR parser recursively but I personally haven't seen one.
Deeply nested instances of right-recursive rules will blow the stack. If the LARL parser has an unlimited stack due to dynamic allocation, that will perpetrate a DOS.
Table-driven LALR(1) with an explicit stack does not make the recursion issue go away. The tooling may provide built-in handling for it which translates excessive depth into a syntax error.
Recursive parsing using the native stack can take steps to protect itself, like by keeping track of the depth, and bailing upon hitting a limit.
Techniques involving obtaining the stack pointer (or close estimate thereof), and comparing it to a limit, are also possible.
