Most of my mando instruments have Allen cast tailpieces. My Morris hybrid F4 has the standard tailpiece in the OP's photo (with the slide-on cover). AFAIK these were first used by Gibson in the early 1900's.
Like others stated I use the sideways hooks for the E strings. I've never had them break at the tailpiece hooks. I think these old style tailpiece are only used for tradition's sake. My 1930's Stahl Banjolin and Regal resonator mandolin don't have that style of tailpiece and they were made for the same strings as the standard Gibson tailpiece.
I say it's your choice to use the sideways hooks or not.
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