Long-time NXT user here.
I remember you could trade fiat on the NXT asset exchange using Coinomat's coinoUSD asset as well as assets representing cryptos (e.g. mgwBTC, mgwLTC) using jl777's multigateway.
I know that Coinomat and jl777 were a big part of what made NXT and its AE so successful in its early days so having them is a big plus for WAVES and WAVES' distribution is probably better than NXT's due to the difference in size of their ICOs but feature-wise, what is the difference between WAVES and NXT circa 2014?
Waves DEX has Matcher which can complete orders in a real time. After completing orders will be placed to next block.
This allows you to achieve a higher speed of work on the exchange. I don't test it yet.
NXT AE don't (I have experience with AE - several transactions).
And important difference at this moment is money from ICO, which allow to develop and promote the product in the future.
The number of projects on the platform Waves is growing already.