Many firewalls drop outbound connections which are not to ports 80 or 443 (http & https); some even drop connections to those ports that are not HTTP(S). FTP may or may not be allowed, not to speak of the active/PASV modes.
Also, HTTP/1.1 allows for much better partial requests ("only send from byte 123456 to the end of file"), conditional requests and caching ("only send if content changed/if last-modified-date changed") and content compression (gzip).
HTTP is much easier to use through a proxy.
From my anecdotal evidence, HTTP is easier to make work with dropped/slow/flaky connections; e.g. it is not needed to (re)establish a login session before (re)initiating transfer.
OTOH, HTTP is stateless, so you'd have to do authentication and building a trail of "who did what when" yourself.
The only difference in speed I've noticed is transferring lots of small files: HTTP with pipelining is faster (reduces round-trips, esp. noticeable on high-latency networks).
Note that HTTP/2 offers even more optimizations, whereas the FTP protocol has not seen any updates for decades (and even extensions to FTP have insignificant uptake by users). So, unless you are transferring files through a time machine, HTTP seems to have won.
(Tangentially: there are protocols that are better suited for file transfer, such as rsync
or BitTorrent, but those don't have as much mindshare, whereas HTTP is Everywhere™)