Using Backbone with ajax requests will be slightly faster than using Turbolinks.
However, Turbolinks will provides SEO by default, whereas you have to do a lot of work to make Backbone and SEO work (See this StackOverflow question)
You'll also have to write a lot of JavaScript if you use Backbone compared to writing hardly any JavaScript if you use Turbolinks.
It's really up to you to weigh the pros and cons and decide which option is better for your situation though.