I auditioned the UERM and JH13 (non-freqphase) universal demo models (along with other JH and UE demo models) leading up to my purchase of the JH13 FP.
I went straight from the JH13 to the UERM and I thought the UERM sounded awful by comparison. Very mid-forward, a little harsh, and with an artificial edge. The JH was smoother and more natural without sacrificing detail. I didn't think either model was completely neutral, but I much preferred the JH's presentation. Take this with a grain of salt, as it was a short demo and I went in fairly certain going in that the JH13 was right for me, and, as I mentioned, they were universal-fit demo models.
Having since gotten my JH13 FP, it's a little baser than expected. I wouldn't call it warm. It's just that there's some emphasis in the lower bass, like turning a subwoofer up a couple notches. I'm used to a very flat sound with my reference speakers, and my reference full-size headphones are AKG K701, so I'm not exactly a bass-head. The JH13s are ever so slightly more bassy than I'd like, but I think they're very close to my ideal for headphones.
Depending on where you live, there's a pretty good chance you can find a dealer that has both JH and UE demos. That'd be best. But I'll tell you that having faced the same decision as you, going with the JH13 was an easy choice. Ideally I would have liked to have tried the Westone ES5 too, but I'd already committed to the JH13 by the time that model was on my radar, and everything I've read since has reinforced my choice.