Overall, I'd probably give it to the Proteus. I was just having this crisis myself when looking to replace my R.A.T. 9 wireless. Amazing mouse when it works, but when it works isn't often. Mine finally died, and I found myself between the above two at the store (after days of forums, polls, and inquiries) before I finally noticed the Razer Ouroboros in the corner and went with that.
Comfort: DeathAdder
It just felt... Natural. Despite how abnormally light it is, I never had trouble keeping a grip, nor was my hand ever forced into an awkward position. When I tried holding the Proteus, it just felt too thin for my preferences. My hands are slim with long fingers and I use a palm grip instead of claw, so the RAT9 was a dream for me and I was looking to replicate that. Neither of these do, but the DeathAdder gave a better experience in this category. This is kind of a make or break for me, so huge bonus points to DeathAdder's body design.
Customer Service: DeathAdder
Nothing much to say here. No other company in this department can hold a candle to Razer when it comes to customer service, especially when combined with Amazon's already generally awesome customer service. Rejoice Razer fanboys. This is the one absolute truth I will afford you. I don't know much about the Logitech and the customer service, but is known by peoples I are asked as 50/50.
Durability: Proteus
Let's face it. As much as we all love Razer's customer service, you tend to end up there for a reason. I have nothing against lightweight mice (though I prefer heavier), but the DeathAdder crosses a boundary, Razer in general tbh, where the products themselves just feel like cheap plastic. 90% of the Proteus owners I've asked haven't had a problem with their mouse that an update hasn't fixed. ~60% of Razer owners were on their 2nd at least, thank Razer for being so kind with replacements. This might be skewed from the sample size (I found about 15 of each), but these were my findings. I myself went through 1, the second I still have as a spare (Regular DeathAdder, not a Chroma)
Performance: Proteus
Proteus allows you to shift your DPI between "I think I'm 86 what is the fancy type writer" and "CSGO Internationals here I come" (really slow to really fast). There's also surface calibration and balance tuning to make sure it plays optimally on whatever surface you're using. Most owners I asked ignored this, but there was that one weirdo from the group (God Bless you Logan) that bragged about how nice it was for him. Finally, you can add a few weights for heaviness, though honestly it's not that big a difference. If you like heavy mice like me, the weights won't do anything for you. It also has a bunch of awkwardly placed buttons you can maybe make use of (Realistically only 2 or 3).
The DeathAdder is pretty much face value. DPI peaks slightly lower, but still super high compared to the average user. Can make lots of pretty colors. Two extra buttons you'll probably never use (but if you do, then good for you). A known-to-be iffy program that whines about wanting to be updated it a lot. DeathAdder tends to have issues with the scrolling wheel.
The Ouroboros caught my eye because it has the sheer width/length that I loved so dearly about my RAT9, and the reviews from 5 minutes on google mobile while in the store showed no serious complaints or issues. It was $139 (around the price of a RAT9), so a srs cash difference, and I'm not a fan of it's abnormally light weight that Razer seems to be obsessed with, but a couple months in and I'm pretty happy with it. Wait, all this is irrelevant. But, ummmm, yeah, if I hadn't got the Ourorobos, I would've walked away with a Proteus.
If I remember what the 5th category I was going to put was, I'll comment with it.
Hope this helps.