I'll weigh in too, though I think everyone has covered the big points.
We've stayed a both numerous times. The only reason I would pick Castle Inn over Candy Cane Inn would be price. Looks like you are talking $38/night, approximately, in savings. If money isn't a problem, I think you'd have a much better experience at the Candy Cane. I'd stay at Castle Inn again to save money if I wasn't going to be in the parks from open to close. My wife doesn't want to stay at Castle again. She loves Candy Cane--it's our new go-to. Here are some comparisons:
Parking: Both have free parking, I think. I'm positive Candy Cane does: one car per room. We've never had a hard time finding parking at Candy Cane. Can be a bit trickier at Castle Inn.
Breakfast: Candy Cane has it, Castle doesn't. The breakfast is good: cereal, oatmeal, juice, boiled eggs, fruit, yogurt, pastries, bagels. There is something to be said for not having to buy breakfast or make it in your room. Is it worth $38/day? Up to each individual...
Walk: Pretty comparable, though Candy Cane is slightly shorter. With Castle you have to cross over Harbor, but it's not a huge deal
Shuttle: This is a big plus for my wife. Her health sometimes gives out at the end of the day and the shuttle has been a lifesaver. Overall I don't think it saves much time, if any, especially going from Candy Cane to
Disneyland since you have a U-turn and a left turn. From Disneyland to Candy Cane it's two right turns and really quick. Even if it doesn't save time, it does save steps if needed.
Rooms/Beds: One of the reasons my wife doesn't like Castle Inn as much are that the rooms feel dark to her. In our opinion the beds are WAY nicer at Candy Cane. They are just so comfortable.
Grounds: Castle Inn is basically just a parking lot and decorated walkways. Candy Cane is super pretty with all the flowers, trees, cobblestone parking lot, wrought-iron work, etc. This is a huge selling point for us, especially my wife. It feels more to me like a "resort" even though it's not of course; Castle Inn is a basic decorated motel.
Pool: Hands down way nicer and prettier than Castle Inn. Our kids loved the pool. The kiddie pool was great for our granddaughter. We take mid-day breaks and the pool was awesome. The hot tub was hot and wonderful at night.
Staff: Both seemed equally nice.
Overall: If you need to save the money even after considering the free breakfast at Candy Cane, go with Castle and you will be just fine. Especially if you don't spend much time at the hotel during the day or evening. If you want a more enjoyable place to stay and you are okay with the extra money, Candy Cane is great. I don't know that we'll ever stay somewhere other than Candy Cane now we've been there 4 times, unless for some reason their prices are way higher than elsewhere. The breakfast, the pool, the easy walk with shuttle backup if needed, the grounds, etc seal the deal for us.
Good luck! Either way you are close to the parks, safe, and will have a wonderful time!