HLS seem to be the more popular format these days and browsers seem to start supporting it natively. I said hls/dash because both formats offers mostly the same benefit compared to just simply embedding mp4 files directly. You can use hls.js for hls and dash.js for dash, or video.js for both.
You say to convert to HLS/Dash, does hls.js support both? Pros cons of one other the other? Make sense to do both?