Both sound very good, and are best among all current high end DAPs and pairing them with amps yields no or very little benefits.
901 in general is warmer, more musical/euphoric, and have fuller sound. Amongst the amp boards you can pick the warmest/tubey type sound with the Classic card, or a more reference, wide staging, and powerful Balacned board. Or you can choice Minibox which is a bit more euphoric than balanced, but less syrupsy than the Classic. Comparatively AK240 is more neutral, analytical, and have a less full sound overall, a few users wanted a more full sound and end up sending it to RedWineAudio for their mod service and try to make it sounding closer to the hm901. Between Ak240 and HM901, which one is "better" can be very subjective. For me, it is the 901.
But trust me, looks/weight/UI are all factors that affect how you use it daily....
You're making me think I really must get an A/B comparison with them somehow. So difficult... Perhaps I should buy the 901 from Amazon and take it to the place I can demo AK240 at again, then send the 901 back if I prefer the 240. It seems so dishonest doing things like that although it's allowed under UK distance selling.
Honestly though the looks/weight/UI are irrelevant to me though. I listen on the train or at work, which means I always have my backpack nearby. I'm too old to care what people think of how my portable gadgets look ;) As for UI if I can navigate a tree of folders and hit play, I'm happy. While the AK240 is undoubtedly a nicer design the HM901 looks fine, it's not bright red or covered with flashing LEDs. I do care about reliability though, I tend to buy one thing and run it into the ground rather than constantly upgrading.
Long shot - is there anyone in the Cambridge UK area who has a 901 I could audition? I have a car, anywhere I could easily drive to on an afternoon would work.