It's hard to talk in general terms but Memcached is threaded so you can saturate your CPUs without requiring multiple instances, and Redis has more advanced features both from the POV of programmer API facing and operations. But if we want to zoom on Reddit itself, the fact of using data structures and changing caching paradigm to really use Redis the proper way, that is, storing metadata in Redis and not just only in their main DB, I suspect would provide a very big boost to Reddit. For some reason Reddit always has been an "anti Redis" shop. I'm sure they have their good reasons, and btw I love Reddit too much to complain, whatever they do to run it, I don't care as long as they provide such a wonderful service to the community :-)
But... their use case is IMHO one that you can accelerate tremendously by using Redis. I ran the most popular Italian Reddit-alike site for years, and I wrote a simple Reddit clone that uses Redis so I had the opportunity of exploring the problem a bit.
Reddit is most definitely not an "anti Redis" shop! If we were to rewrite it today, we might start with Redis. We've just put so much work into making memcached reliable and easy to understand for developers that the possible benefits of switching to Redis for many of these use cases don't outweigh the operational knowledge we have from years of running memcached at this scale.
That said - we use Redis in at least 2 (soon to be 3) capacities across the site for different services (outside of the monolith) and it works really well.