I guess what he means is that 2 puts will also give you double gamma,double vega (same as 1 call, 1 put. ). So in that sense, the straddle is no more or less preferable than 100 shares and 2 puts. But I will wait for him to answer.
That is correct. A straddle = a put plus a call = put + synthetic call ( put + stock). The practical difference will be dividend exposure, balance sheet usage, and not having the need to ever short stock. Two options have twice as much vol risk as one option so you can't compare a straddle to one call/put delta hedged.