The only way it makes sense to buy them both is if they have the same IV, otherwise just buy the one with the lower IV, as IV differences in the same underlying reflect the relative over/under-pricing of the option.
E.g., if we assume that the ATM SPX option is efficiently priced, meaning that over many trades, buying the ATM results, before commission and slippage, in breaking even, then buying the options with the higher IV - usually ITM for calls and OTM for puts - would result in a loss. This explains why selling OTM puts and buying OTM calls tends to be profitable when done with proper money management.