親子丼を食べることに決めました。 is more grammatically correct, but to be honest with you, still it sounds weird for me, but maybe only for me. The following site might helo you understand these two. http://japanese.stackexchange.com/questions/2772/%E3%81%93%E3%81%A8%E3%81%AB%E3%81%99%E3%82%8B-vs-%E3%81%93%E3%81%A8%E3%81%AB%E6%B1%BA%E3%82%81%E3%82%8B することになる:is influenced by others more than when you use することに決めたよ。Therefore, the decision is more likely made by others.

They are the same to me. I would say the second one as it sounds more natural to me.

親子丼を食べると決まりました。 It is said just after some argument. That was not only meal but any plans like "having a lunch or continuing what we are doing". There ware always other options end up deciding to eat OYAKODON. 親子丼を食べることになりました。 It could be same different. But also another meaning. It does not always need argument nor other options to use this sentence. As Yamada's correction, this sentence is influenced by other factors including your situation.