IrinaAlexandra looks more rounded more finished if you know what I mean and I prefer this over IrinaAlix Alexandra is one of my top three favorite girls names so I am biased in favorour of it Alix seems too short too nicknamey for my tastes but then I tend to prefer longer forms over short forms
I'm inclined to agree that IrinaAlexandra looks more polished. It just looks more complete. The more I look at it, the more it seems like the perfect "Irina" combo. :) _____