There is no difference in sound quality between 88.2 and 97 KHz (or any higher rates) because they both extend miles and miles beyond any human hearing range. If you hear a difference, it will be because your converter (DAC) is not working as well as it should be with one of these sample rates. A good quality converter should sound equally good at any higher sample rate. However not all converters are created equal and some are good at covering one sample rate, but not so good at converting another. The good news is that converter technology gets better every year.
Reasons to choose one over the other
You might want to consider the primary destination of your audio. If you intend to release on CD, 88.2 KHz might be a better choice to record at. Conversion from 88.2 to the CD sample rate of 44.1 KHz involves much simpler calculation and is therefore likely to be a cleaner conversion than moving from 96 to 44.1 KHz. However if your primary destination is film or video, 96 KHz might be a better choice as the standard for video is 48 KHz, which is an easy conversion calculation from 96.
Having said this, if you use world class sample rate converters like iZotope RX5 which we use at Heron Island, you will not hear any degradation converting from either 88.2 or 96 to either 44.1 or 48 KHz.