Hardware are not the same. Even though they appeared to be. Linode has both faster CPU and SSD.
Linode's plan offer more SSD space* and Transfer.
And Linode is based on Xen, while DO is based on KVM.
Linode has a much wider selection of OS images.
In Most cases, Linode offer better stability, and higher quality network.
Linode has IPv6, while DO is only just started rolling out in selected DC.
Linode offers pooled bandwidth.
Linode has Add on like managed instance and NodeBalancer.
Linode will automatically setup your instance in different server hardware. DO has the features planned for a long time, not sure if it has been implemented yet.
DO listed they have private networking, much like their Ipv6 is only available in certain location. I am pretty sure Linode has it as well, but i could not find any concrete info.
DO accept Paypal, while Linode dont.