It's an interesting conundrum. Looks like the 3.5mm is purely voltage-limited even driving 32 ohm loads. The 6.3mm has higher voltage output and gain but will run into clipping slightly below maximum 3.5mm level with such loads.
If you're using the 3.5mm, you can rely on the output being able to back up its voltage capabilities with current output, even at +7 dBu out (giving 90 mW into 32 ohms). Not so for the 6.3mm - if purely voltage limited, it would be able to dish out almost 220 mW into 32 ohms, rather than just 60 mW, so it's clearly current-limited first. You may have no other choice than using it if you are limited by gain, i.e. your digital levels are so low that you wouldn't reach the power limits of either output anyway, however you need to be aware of the possibility that you might run into clipping.
This interface is decidedly not primarily designed for driving insensitive planars - you can shoehorn only so much headphone power into a high-performance interface with a 5 V @ 700 mA total power budget. You're expected to be using the 3.5mm for IEMs or lowish-impedance dynamic driver headphones like your K371s, while the 6.3mm is a better fit for medium-high impedance models like 150-300 (maybe 600 ohm) Beyerheisers.
If push comes to shove and you find yourself running out of volume on the 3.5mm jack with your planars, you can always run it into an external headphone amp still. A Topping L30 II is hard to beat for the price. Then we'd be talking 2-3 watts, not mW.