Is restoring a mysql database backup faster at removing white space than running OPTIMIZE?
Both will achieve essentially the same thing. If your exact db version doesn't offer online OPTIMIZE then the dump and restore could be useful if you restore into a new table and then DROP the old one and RENAME the new one, allowing concurrent selects during the import. Regarding the speed, the dump and restore might be a bit faster but it's probably not a huge gain. I prefer it if I'm working with a version that doesn't support online OPTIMIZE. 

As Rick James mentioned this sort of thing isn't often necessary, but I have seen it help to bulk re-balance indices on tables with columns struggling to keep up with a large number of concurrent updates.