When comparing BYOND vs Wave, the Slant community recommends BYOND for most people. In the question“What are the best 2D game engines?” BYOND is ranked 29th while Wave is ranked 33rd. The most important reason people chose BYOND is:
BYOND is in active development and updates are released constantly.
Specs
Ranked in these QuestionsQuestion Ranking
Pros
Pro In active development
BYOND is in active development and updates are released constantly.
Pro Easy to use
The software itself is very easy to learn and use for beginners.
Pro Helpful community
BYOND's community is relatively large and extremely helpful. Any question a beginner or an experienced user may have is quickly answered.
Pro Large Community
Fairly large player base and multiple games to play.

Pro Extensive learning material
In addition to online API documentation, the Wave Engine team provides tutorials via IndieDB, plus sample projects and "QuickStarters" via GitHub.

Pro Supports coding in C#, F# and Visual Basic
Wave Engine explicitly supports all three core .Net Platform languages.

Pro Oculus Rift support
The Wave Engine team provides an official, open-source Oculus Rift extension via GitHub.

Pro Many components are open source
Several core components and official extensions of the Wave Engine are publicly hosted on GitHub.
Cons
Con Highly supports multiplayer, but can make solo games ready for download.
Con Exclusive programming language
The language is known as DM, and is modified using Dream Maker. It is an object oriented, interpreted language, which closely resembles C++, Java and PHP. More information available in the DM Guide.

Con Mandatory splash screen
Games and applications made with Wave Engine must display a splash screen advertising it. No splash-free license option is available.
Con Not many tutorials available
Con Outdated UI
The UI looks like it is from Windows XP days. A refresh is much needed.
