Since NXT is standard proof of stake, just with some proprietary bandaids on top of it to try and mitigate it's core problems, it's mostly going to fall under this comparison I did here:
Standard proof of stakeA) Coin ownership is network control, leading to enormous security risks since money tends to congregate in large financial institutions, meaning there probably has to be a separation between block validators (miners) and coin owners or the currency itself, unless you want Exchangenamehere or Goldman Sachs to always control the network from their deposits.
B) Besides the above problem, you also have history attacks, nothing at stake attacks, etc.
C) Coin age variable had to be dropped for security, so the largest stake holders essentially reap all stake rewards leaving no reason for anyone else to stake at all. Some coins claim to solve this problem with pooled staking, but people tend to be lazy and things like this require people to be proactive to secure the blockchain.
D) Stake reward tends not to be that high, and keeping coins online out of cold storage is a security risk, so even if it was the world reserve currency, a large percent of people would just not do it, leaving network control to large exchanges and banks. There are just a lot of factors that tend to always place the network control in the hand of a traditional bank.
E) One of the main draws of PoS is that you can validate blocks at home on cheap equipment and not use huge energy at the same time, yet this would also limit it's transactions per second to low speeds under all current implementations, having only enough to function as a clearing mechanism between banks or having large fees to use if the currency became big and still wanted to be staked in a home environment.
DPoS - Delegated Proof of Stake (Bitshares)A) Low overhead and large transaction processing ability rivaling entities like Visa in capacity and speed
B) Possibly the best platform for running a decentralized exchange
C) Deterministic number of block validators (101) that if all actors are unique, is much higher decentralization than Bitcoin PoW pool mining, although reputation and identity can be gamed for the same person to pretend to be multiple actors.
D) In order to avoid reputation or identity gaming, some people such as Tim Swanson say the 101 block validators might have to be publicly known NGOs. My personal opinion is that some of them being NGOs would probably be a good thing, but it would probably function fine with a mixture of NGOs, businesses, publicly known individuals, and anonymous individuals from many countries.
E) Delegate voting requires people to be somewhat proactive, and people are generally lazy
F) Some people claim this system mirrors the federal reserve branch model. I don't have enough in-depth analysis of upward mobility in the federal reserve system, but I imagine it to be extremely low to non-existent, while Bitshares DPoS would probably be exponentially higher.
G) Has USD pegged assets. Some people claim this would be a derivative backed by itself. Larimer claims the pegs hold fine as long as the network itself has value at all. Analyzing exotic derivatives is not my speciality, and there are several ways to implement things like this, so you'll have to analyze that for yourself.
H) Anonymity functions in progress:
http://bitsharestalk.org/index.php/topic,17687.30.html 
