I think you might be able to "Export" your tree from Geni to your computer and then upload it to MyHeritage?
There are limits to the amount of data Geni lets you export.
Unless there has been a recent policy change you cannot upload data into Geni except by typing each profile in manually.
Try researching "GEDCOM files" which is what the exported data is known as.
Geni and MyHeritage are two different websites and there are no plans on mering them, even if MyHeritage is the owner of Geni.
The main goal on Geni is a world tree, http://www.geni.com/worldfamilytree, where MyHeritage is individual trees.
That's a shame there is no easy way to have the same family details merge from Geni (that I used first and has up to date information) to MyHeritage (that I joined later for their DNA and have not time to copy Geni details across).
So from a wider point of view, with my cousins around the world, it seems best to use Ancestry, a much larger site that most people seem to use.