I've always used my Chromecast with WatchESPN because it's search feature was better than the Rokus. Didn't notice it when Roku killed the app but it's gone now and all integrated into the ESPN app along with the ESPN+ content. Search feature still looks non existent though.
I've had generally the opposite experience. The app UI has generally been better on Firestick compared to Roku. Some of the reason is Amazon is a lot more open with it's technology than Roku (per a friend who is an engineer at Roku). My Roku has worked just fine, but I prefer the app UI on the Firestick better. I recommend getting at least one of each and determining which one you like best.
I've always used the ESPN app on my phone or tablet to connect directly to my Chromecast, works pretty easy, and I like easy.
With the bigger nationally televised games I've had issues streaming. Cuts out, poor picture quality, etc. Not sure if it's the app, ESPN, my internet connection, or just the fact so many people are streaming a particular game (MNF, larger college games, things like that).
Just a reminder to all that you are generally best off to hard wire your streaming connections for optimum performance, particularly if you have obstructions between your TV and router. It is not as hard as you may think; MoCA adapters work right through your cable lines and give the speed you need.