Hello there, imagotech.
The following Knowledge Base article offers up some great recommendations for successfully migrating data from an older Mac to one running Mavericks:
Thanks for reaching out to Apple Support Communities.
I am having the same problem, although it is the older mac that is crashing.
The article you supply is great for beginners (plug in power, run updates, etc.), but doesn't address the root problem (crashing). Assuming the suggestions in the article are followed and one of the machines still crashes, what next?