Xperia Transfer, Google sync

My old mobile is xperia z3, my new is xperia xz1. I bought the mobile today and the main reason was that the internal memory of the old is full, there are about 30kb left on the internal memory! For a long time I have cleared and transferred from the internal memory to the card but something just keep on eating up the internal memory (it's not me I just add a little text now and then). So I bought a new phone with a proper internal memory.
And now I would just transfer the old content to the new mobile phone and solve my problem - and it didn't work. Because that stupid program refused to even work at all, it wants an update first, and that bloody update wants at least 500 Mb free internal memory...

By the way I have also tried synchronization thru my Google account but for some reason it just didn't work.