I have dealt with neck and shoulder pain on and off for years, mostly from long hours at a desk and sleeping on the wrong pillows, so I can definitely relate to what you are describing. A bad pillow can quietly ruin your sleep and you only notice once the pain becomes constant.
Both of the pillows you shortlisted are actually solid choices, just for slightly different reasons, so you are not chasing hype here.
The cervical contour memory foam pillow is very good if your pain is clearly coming from lack of neck support. The shaped design helps keep your neck in a neutral position, especially when sleeping on your back or side. When I switched to a similar contour pillow, the biggest improvement was reduced morning stiffness. It does take a few nights to adjust to the shape, but once your neck settles into the groove, the support feels very consistent. As long as the foam is good quality, these pillows usually hold their shape well over time.
The Coop Home Goods Crescent pillow is also an excellent option, especially if you change positions during the night. The adjustable fill is a big advantage because neck and shoulder pain often comes down to pillow height. Being able to remove or add fill lets you fine tune it for your body and sleeping style. The crescent shape is particularly helpful for side sleepers because it gives your shoulder space while still supporting the neck. In my experience, adjustable pillows tend to work better long term since your comfort needs can change.
One important thing to keep in mind is that no pillow is a magic fix on its own. Mattress firmness, sleeping posture, and even daytime posture all play a role. That said, both of these pillows meet your requirements for proper support, side and back sleeping, and durability.
If you prefer a structured, guided feel that keeps your neck aligned every night, the memory foam contour pillow is a great choice. If you want flexibility and the ability to customize your comfort, the Coop pillow is hard to beat.
Either way, you are starting with two genuinely good options. The key is giving your body a week or two to adjust and making small tweaks if needed. That is usually when the real improvement shows up.