I still think of Linode as more of a "real" type hosting environment, in the time I used them I didn't didn't notice any difference from actual bare metal servers. If I didn't know better that's what I would think they were.
DO, to me is much more of a "toy" and experimenting type of service. I have tried hosting things on "droplets" and had strange issues, dropping, outages etc. Not frequent of course, but over say a week or two of uptime. I'm ok with it because it's $5 and what else would you expect? But I wouldn't think of hosting any real sites on droplets personally.
It's just my opinion and many people I've talked to have had the same experiences. Both are great services for different applications.