Can't comment on DT1350 but I have two T51i (one with stock pads - better, the other with T50p pads - worse) and MH30. I like both, but prefer the sound of Beyers with most music. Agree that MH30 is bassier and sounds darker. There is a way to change that with different earpads, but you'd need to make a metal adapter ring to use 3rd party pads with them. I actually got such rings and can use over ear pads with MH30 - less bass, better clarity.
Beyerdynamic also has better comfort. MH30 has more pressure on ears (clamping force) and a harder, less comfy headband top - it's not bad, but not nearly as good as Beyer T51i. Also, my ears get a bit hotter with MH30. I read that the comfort of DT1350 is not as good as T51 (much more clamping force), so the difference might be a smaller between DT1350 and MH30.
Both headphones look good and are well built, but here MH30 clearly wins, it's a work of art. I have never seen another headphone that's so beautifully made. Frankly that's the main reason I bought it and it does not disappoint. I'm happy to own them. But they are not my daily phones.
MH30 do have the advantage of a detachable cable. Stock cable is OK and you can use 3rd party cables without any problems (no custom locking mechanisms or narrow openings). And there are sockets in both cups, so if one socket develops a problem, you can still use the other. Beyerdynamic (DT1350, T50, T51) have fixed cables. Not sure about DT1350, but most Beyerdynamic cables are either too long and bulky (pro and bigger home headphones), or thin, flimsy and break easily (portable consumer headphones). Both T51i that I have needed cable repair. Recabling them is doable but not easy: pads are glued on, drivers are pushed in and not easy to remove from cups, and I hated soldering cable to very small solder posts on these drivers, it was almost like soldering cable to IEM drivers. These are not repair friendly headphones.
But parts availability/customer service is much better for Beyerdynamic, at least in Europe. I can buy virtually any Beyerdynamic part locally without much hassle (even for many long discontinued headphones). There is local warranty and post-warranty service, at least in my country there is. For Master & Dynamic there is a single parts webstore for the whole Europe (I assume with one source of shipment = longer waiting period). I wanted to buy Alcantara earpads from them. They are "temporarily sold out" at least since last year and I didn't get a response to a simple question (asked in January) concerning their future availability. When they run out of regular pads, we might have the same problems as with Philips A5Pro (replacement pads not available and never will be, using 3rd party pads not easy due to a custom mounting ring). Also, you can order any part you need from Beyerdynamic (including the whole headband assembly, headband cushion, replacement drivers). The Master & Dynamic store only has earpads and cables. I asked about other parts (specifically headband padding) but they don't answer emails.
BTW, pads for MH30 (50 EUR) cost more than twice the price of Beyerdnamic pads (20 EUR).
So if you want one headphone that you will use on a daily basis and not worry about it becoming unusable when the pads wear out or a driver goes, I would get the Beyerdynamic. Especially if you're not a basshead. But I would probably go with T51p or T51i, not DT1350 (which I did) - from what I read, better comfort and they sound more fun.