They don't really sound similar to the 1R despite being in the same price range. It honestly depends on personal preference. Here are my impressions:
Now this is from memory - while the Z1000 was/is generally well-received (it is a very good can) it just didn't suit me personally. It is detailed across the spectrum, on the slightly warm side of neutral, but my main issues with them were that it had some peaky treble and not enough bass impact. Coming from using the HD25 daily in portable use (on the train and loud environments) it just didn't have the right sound sig for me. At home I appreciate them much more, for the commute not so much. They have very nice mids though.
The DT 1350 - this is a can I bought, sold, and recently reacquired because I missed its unique, neutral, high end portable sound sig. It's a pretty flat headphone, very very detailed, DEEP and detailed bass and nice unfatiguing highs. They isolate so well for portable use so I didn't mind the lack of bass punch in comparison to something like the HD25. I'm not saying they lack bass impact because they're fine in that aspect but they're very neutral overall. The mids are amazing though - very lifelike vocals.
In comparison to the 1R they're a different flavor for sure. The 1R to my ears are more full-bodied while the DT 1350 is leaner. The 1R is a little more warm and musical to my ears. They're just a bit more fun to listen to. I find the 1Rs to be very detailed as well and the soundstage is a nice relief after using on-ear portables for so long. Imaging is great as well. The bass is detailed with good impact but may not be as seamlessly detailed as the DT 1350. The mids are beautiful and slightly warmer and the treble is crispy and sparkly without being strident to my ears. I've been on the hunt for a portable circumaural for longer than I've been on HF and I was really not expecting to like these as much but I think these might be keepers.
I would suggest auditioning these cans for yourself if you have the chance. I personally love the DT 1350 and 1R for both their strengths and signatures. The can that sounds more natural and musical to me is the 1R but I don't think I will let go of the 1350 for its detail and great deep bass detail. Both are great cans.
Anyway, these impressions are just due to my preferences so take them with a grain of salt. Hope you get to try them all out and hope this helps.