I can't restore backup to my 5s

I bought 5s. I had iphone 4. My iphone 4 has ios 7.1 and my new 5s has 7.0.4. In this case itunes prevents me to restore my previous backup until I update my 5s to ios 8.4.

Now I looked up to some speed tests between ios 7 and 8, it turns out that ios 7 is faster on 5s.

What can I do now ? is there any way to transfer my data (Contacts, notes, messages) to my new 5s without itunes ?

or is ios 8.4 good and speed enough on 5s ?