It all depends on your version of 'secure'. If you mean problems like someone mining a fake block, or doing double spending and things like that, then yes, they are all equally secure! But if you mean the stability, availability and reliability of the network, then depending on the environment in which they are deployed, the 'secureness' varies.
PoW, PoS, and DPoS are all consensus mechanisms in an ideally trustless distributed network. When you think of then, you have to put them in the context of the entire network in which all the participants come together, it is the glue which builds the macrostructure of the network nodes. There are multiple factors at play if we discuss these consensus mechanisms, including, distributed systems, economic incentives, network participants, computational complexity, etc. In that sense, your question is too broad, but still, some general principles can drive the idea home.
First and foremost,
No one can build a fake blockchain i.e. problems like double spending, block-tampering and etc. will not be compromised in any of the mechanisms above. This property is a direct result of the block chain technology.
In that sense, they are are all equally secure. But....
When the overall health of a network comes, depending on the participants in the network, you might want to choose one over another and there are some attacks mechanisms possible, but they are all concerned with the 'whole' network.
Proof of Work is computationally heavy, hence thwarts attackers from controlling the network. The famouse 51% attack is still possible. But because it is computationally expensive consensus mechanism, a lot of energy is wasted.
Proof of Stake works by choosing participants in the network based on their stake in the network to mine a block. The more stake you have, the more likely it is that the network will choose you to mine the next block. But because you have more stake in the network, you'll lose your own equity in the network and hence you won't do anything bad to the network. It allows a quick solution to the consensus problem on the basis of incentive and prevents wasting a lot of energy as is the case with PoW. PoS is also prone to 51% attack and a beautiful problem called "nothing-at-stake" is also hypothesized by some.
Delegated Proof of Stake uses the notion of governance for achieving consensus. The miners (witnesses) are chosen (voted) by the other participants in the network, and they keep the blockchain going. Ideally, the voting mechanism always keeps on going too.
Now, you can see that the security of the networks using any of the mechanisms mentioned above is exactly the same and is more of a subjective decision- they all have weaknesses and counter-measures to make up for the vulnerabilities at the same time.
