Moving data from Mid-2010 iMac to Late 2015 iMac
Wired ethernet (gigabit on both ends) will be every bit as fast as Firewire to Thunderbolt and without the cost of the adapter.

Depending on how noisy your Wireless environment is, you might have a limiting factor in the speed of the old iMac hard drive that's lower than WiFi throughput, but wired ethernet is so much more reliable, I'd do that if you can.

If you decide to try a wireless set up, use the fast new Mac to create a WiFi network and join the old iMac so that all the radio speed is dedicated to the transfer if you wanted to go that way with more than 10 GB of files to transfer (presumably).