For one, I greatly prefer the comfort of the Stax (I have SR-Lambdas running through an SRM-T1 amp). The K701 was never uncomfortable to me, but the Lambdas are lighter, and their fit better mimics the shape of the head. Nice design.
I liked the large soundstage of the K701, but I always felt it was unnatural. Instruments felt like they were "too big". Mandolins sounded the same size as guitars, and basses filled the whole picture. The Stax has a large soundstage, but with much more precise imaging. The relative and absolute size of instruments is more realistic, which I enjoy.
The K701 has great detail, but it gets it through a tipped-up frequency response. There is just too much high end, and it makes the rest of the presentation suffer. Lambdas have all the detail that the K701 have, but with a better balanced frequency response. That gives them slightly warmer mids, though they are still described as "cold" sounding.
Neither of them has towering bass to speak of, but the bass from the Lambdas was preferable to me. I felt it was more detailed and realistic sounding, which helped make up for the small lack of quantity.
That's a pretty brief summary -- others have written more, and done so far better than I.
I'm just asking, did you let the K701 burn in properly?
And what type of music do you listen to with the Stax.
And I was reading, with the new Stax headphones of today, they are based on the Lambda design. But do these new stax phones have better improved technology over the Lambda phones?