We have stayed at both (most recently May '18 at DI&S, Oct '18 Anaheim), location is my main priority, but price is a close second. I am not very loyal to one place over the other - as long as it is a good price, clean and within walking distance to DLR (The Anaheim is as far as I would go) I don't care which one it is. We have stayed at DI&S (3), Tropicana (1), HoJo (1) and Anaheim (1 and an upcoming trip in Nov)
Location - the DI&S is so close! But The Anaheim is just a short walk, really just a few more minutes than DI&S.
Breakfast - we don't do breakfast in Harbor hotels since they are usually pretty horrible so we don't care that the Anaheim does not have one.
Pool - Anaheim hands down. We are never even tempted by the DI&S pool, you can smell the chlorine from the outside.
Rooms - DI&S has big enough rooms, we just go to shower and sleep so don't need anything fancy. The Anaheim has bigger rooms with king beds and the one we stayed in (ground floor) had an enclosed patio.
Price - The Anaheim can be found for a good price even close to arrival date. For the DI&S the earlier you book the cheaper it is - they sometimes have specials but you have to keep an eye out on it. Last month we decided to go back to DLR in Nov - last minute for us - and I found the Anaheim for $67 on Hotwire (it has since gone up to $102), DI&S is in the $175+ range for our dates. For $100 less a night I will walk the extra block
The Anaheim does have Pizza Press on property and they also have a bar in the lobby.
DD and I stayed at the Anaheim by ourselves for last Halloween. Even walking back after the party we never felt unsafe. There are tons of people walking around from hotels nearby.
For a first trip I would recommend DI&S, but once you are familiar with the area The Anaheim is a bit nicer with just a little further walk.