Downside: if you have any kind of home network, running your own recursive DNS probably implies running your own DHCP, which isn't normally a consumer alternative (you could do it using settings on a domestic router, but not if it's crippled or locked-down). Also, DNS caching shouldn't be so effective (but I haven't noticed that effect).
Upside: all kinds of problems resulting from relying on DNS servers controlled by others disappear. You're not relying on them any more.