What are new features (or problems) that this cryptocurrency offer (or really solve) relative to other existing coins? Monero, Bitcoin ...
That's a good question that's often overlooked. The three biggest problems that Decred takes note of when looking at Bitcoin are issues grouped under (1) project governance, (2) funding development, and (3) proof-of-work (PoW) miners having too much power. These observations are documented in a blog post by one of the stakeholders (c0) in Decred's multi-stakeholder development ecosystem. In addition, these stem from over 2.5 years of active contribution to the larger ecosystem by Bitcoin developers employed through c0 - the majority of guys who built and maintain btcsuite. This is the first time in history that such a group of developers - who come from a Bitcoin development environment - are sailing into alternative cryptocurrency waters. Alts have gotten a bad rap - for good reason - but that does not mean all alts have to carry that burden. It is possible to create a future where a symbiotic technological relationship exists between cryptocurrency systems. Good things in Bitcoin come to Decred, and good things in Decred will go to Bitcoin. That's the crux of the relationship Decred envisions between it and Bitcoin.
To work backwards, the technology hopes to address (3) by hybridizing PoW with proof-of-stake (PoS) where PoS becomes a "2nd authentication factor" on the content of blocks created by the PoW miners - and thereby providing a check on the power of PoW miners. PoS can effectively force soft and hard fork upgrades by voting against PoW blocks that do not adhere to the new rules - which creates a notion of continuity across forks that is not possible when using pure PoW. Furthermore, PoS helps to "democratize" the process of deciding what software upgrades should and should not happen. Finally, PoS rewards create an incentive for users to hold their coins and participate in the PoS consensus process. As a summary, these ideas are not possible in a pure PoW system - which has its merits, of course - but Decred argues we need a more robust consensus system. That is the heart of the technological system. There are endless architectural differences between btcsuite packages and the Bitcoin Core client that have been built, tested, and documented over the years - and improvements are worked on every day. All of that comes to Decred and dcrd would for example push contributions back to btcd in the future. If you are curious about (3), definitely have a look at DTB001 as a .pdf or on the wiki.
When we talk about (2), it becomes critical to generate funding internally. Bitcoin has to rely on funding from external parties, where transparency isn't always possible. This may have a corrosive effect on the overall system if the influence of those parties are not aligned with the interests of Bitcoin users. By including a development subsidy as a consensus rule, what is essentially said is that the financial influence over the project is shifted to the users where you don't have to rely on donations. If the users don't agree with the direction of the project, they don't mine and use the software, which acts as a check on those who have to administer it. What you do end up with, if handled responsibly, is a self-funded development mechanism that remains sustainable as the network grows. The upside in Decred's case is that there's a legitimate track record of quality development by way of btcsuite, as well as the other free and open-source projects the devs have produced that haven't been mentioned here yet.
Finally, (1) is where all of us as a community will play a very active role. The current proposal is for a meritocratic form of open governance. Bear in mind this is a proposal, so it's open for discussion as well, and will mature with community input. The goal is a system where your contribution, not your status, carries influence and has attrition built into the design. This is to say that if you contribute lots of code, but then stop, that influence diminishes - so you can't call shots just because you contributed lots in the past. It must therefore remain consistent. This gives newcomers the ability to become just as influential as people that were part of Decred from the beginning - entirely based on continued contribution to the ecosystem. This is again based on observations in the Bitcoin development ecosystem over the years.
Hopefully that gives some insight what Decred is about in terms of its relationship to systems like Bitcoin's. Not entirely familiar with the deeper systems involved in Monero, but if anyone would like to add in where we can improve as a system or technology relative to Monero, that would be very helpful in guiding development. tacotime, for example, represents another stakeholder in the multi-stakeholder ecosystem described above, and has been very active in Monero technologically - so he may be well aware of how the finer Decred points operate relative to that system. Having said that, any new stakeholder from Monero can plug into Decred without fear of missing out on the early Decred days, same goes for anyone. The goal isn't to create more competition, it's to bring an entirely different way of thinking about how we relate to one another.
