How is DxO Optics Pro Elite any different than photoshop when it comes to white balancing?
If you mean adjusting WB directly in Photoshop, there is a significant difference. DxO is performing the adjustment on the RAW file, meaning there's no loss of image quality when you alter the WB. Photoshop is adjusting a converted file, meaning changing the WB degrades IQ. But, if by 'photoshop' you actually mean Adobe Camera RAW, then it's probably no different - you have the same two adjustments, temperature and tint, and ACR is working on the RAW file.
Generically speaking, DxO is analogous to Adobe Camera RAW, not Photoshop. ACR converts RAW files into a format that either Photoshop or Lightroom can use for subsequent editing. DxO is not an image editor, it's a RAW converter. But IMO, it does a better job than ACR at RAW conversions, in part because the DxO corrections are generated from laboratory testing of specific camera+lens combinations. ACR now offers lens-based corrections as well, but they are not as accurate (they are estimates and apparently some are derived from user-submitted profiles). Also, ACR does a fair bit of 'black box' processing based on what Adobe engineers think make images look good, and those changes are automatic, invisible, and can't be turned off. DxO can has presets with the same goal, but you can choose to use them or not.
Personally, I really like DxO. I found that it certainly does a better job than DPP at RAW conversions (comparison HERE