I am beginning development on a new AppEngine application using Groovy. It will be medium-sized and use a number of AppEngine services. It will have both a regular and a mobile website, using HTML 5 and JQuery.
Which of the two frameworks suits my case best? And why?
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I am not directly comparing Grails vs. Gaelyk on App Engine but maybe my blog posts will help you in making a decision: http://bit.ly/9BRQRP. In general you are better off with Gaelyk because the cold startup times are lower (assuming you don't want to pay for a reserved instance). Gaelyk provides a nice abstraction layer on top of all the App Engine services which makes using them easier. The Grails App Engine plugin only helps you with enabling your Grails app for deployment on Google's platform.
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I spent long time trying to make Grails work with GAE last year but I encountered lots of problems with long cold start... Grails took more than 30sec to start and at this time, it prevented Grails from being used with GAE. I asked some questions on Grails forums but no answer so I decided to find another solution and found Play! that works like a charm with GAE. It is not Groovy but pure java and I find it is the best thing I've seen around Java for a long time. So Gaelyk is a nice solution if you absolutely want Groovy but I'm a big fan of Play! now and I would advice to take a glance at it ;)
With Graeme (Grails project lead), we looked recently into making the latest Grails run again in App Engine, and we stumbled across some OpenJDK bugs that prevent the latest Grails from even starting on App Engine. So till those issues are resolved, and we are able to resolve other potential issues that may arise, recent Grails versions won't run properly, if at all, on App Engine. So Gaelyk seems to be the sole "Groovy" option on App Engine for now.