I have read that the battery life is OK on the new AK. Maybe 11 hours, but check!
I think the A&K will overall be better sounding, but it comes down to preference. They say A&K tend to be a bit forward and exited. I would not know, because I have never heard a single A&K unit. If I were you, I would go by pro-reviews, and user reviews. What HiFi reviewl the a&norma SR15, as 'full and lush'.
The ZX300 is quite neutral, I think. Not screaming hot on detail, and not laid back...…...ZX300 battery life is very good. … It does bug me when the EU volume limiter kicks in about once a month. It stops playback, and pauses until you press OK. (OK that you know you are over EU recommendation volume.)
I think the A&K will have more volume, in single ended at least.
I wanted the Sony for battery life, plus users love it. What pro-reviews there are, were very positive about the ZX300. What HiFi's review of the ZX300 was only four-star. However they only ran it in over a weekend, while Sony recommend 200 hours to be sure.
If I were starting again with no DAP, I would audition the A&K - no question about that. (I would wanted DAP I had to pair with a Chord DAC in OTG mode too. You might want to check that.)