H.264 is still the most used codec; mostly because almost every player and device supports it. Indeed there are other codec that can provide better quality results at the same bitrate (or same results at a lower bitrate), but regardless: with 8Mbps you should see a quite decent picture quality with H.264. My guess is that it’s rather the encoding parameters that you may need to review and tune.
I recommend to look up and read some articles from Jan Ozer, who is a renowned expert on encoding. His advise is basically: measure twice, cut once. Here are some links that may help you:
https://www.streamingmedia.com/Authors/4247-Jan-Ozer.htm
https://streaminglearningcenter.com/