Vests have always been popular with fly anglers, especially in the freshwater trout scene. With all of the storage they offer for all kinds of doodads, it's easy to see why this is. Despite the undeniable handiness of vests, I've never been a huge fan of them—even when I trout fished much more in the past. In fact, I can't remember wearing a traditional-style vest outside of when I was just starting out in the sport!
I currently own something from Orvis that's real similar to a traditional vest, but it's technically just 2 large front storage pouches and a small backpack all connected together with some thin strapping/shoulder straps. It can get kind of bulky when filled up, but I do like to use it a handful of times each year when I fish Pyramid Lake in Nevada. Why? The main reason is so I can take both my tackle (front pouches) and a full lunch with several waters (backpack) with me. I typically fish quite a ways down the beach from where I park, so I need to bring everything with me so I don't have to walk a mile back to the car.
Getting more back on topic, I mostly forgot about vests once I discovered packs and slings. As an absolute minimalist when I fish (usually), I prefer bringing the least amount of gear and using the smallest, least intrusive means of storing it all. Anglers often bring way more than they'll ever need and it can make for more of a hassle than its worth. Less items makes it easier for me to quickly locate what I need and offers better mobility and comfort overall.
Let me share some things that might help you decide on whether you want a vest, sling, or pack.....or maybe all three!
Deep Wading: Do a lot of very deep wading? If so, choose wisely. Waist packs are most certainly out, but chest packs, some slings, and yes, vests keep your gear high up on your body and out of the water. Something that's built waterproof might be a good idea here as well!
Hot Weather: While a vest may offer a hair more warmth in cold weather, a small pack or sling is awesome for fishing in warm temps since they are small and keep most of your upper body free and open to breathe.
Simplistic Design: For my typical types of fishing, I bring the following items: flies, a leader spool or two, hand sanitizer, forceps, pliers, and a pair of scissors. Those few items simply do not require a vest, so a very simple pack with a large main compartment and a couple small outer compartments works great.
Stay Clear: One thing I don't like about wearing a vest (or chest pack) is all the bulk and things hanging from it are right in front of me. Not only can the line catch on them, but I just don't like the general comfort and I feel it impedes my movement a bit. A pack or sling that can be worn to the side or even behind me is what I like since it stays totally out of the way. Sure, line can still find a way to hang or tangle once in a while, but its usually not a constant bother. If I need an item, it takes about 2 seconds to pull the pack or sling to the front of my body for easy access, and it can be returned to its out-of-the-way position when I'm done.
When Nature Calls: When you're wearing waders, bathroom breaks can be a pain—even more so if you're wearing a vest since it'll likely have to come off to unfasten/fasten the suspenders. Many packs or slings come off super quickly which just makes the whole process a little easier.
Lots of Extras: If you have a lot of little extras you like to wear on the very outside of a vest, chances are a lot of packs and slings can accommodate them as well. Many of them come with various hooks, velcro straps, and loops that you can tether smaller items to with retractors, clips, or other means. Some packs even have built-in net holders!
Padding/Support: Any well-designed vest or pack should be comfy to wear. A quality pack meant to be worn across the shoulders should have a good, soft shoulder pad that provides a nice cushion for a long day. In addition, there's also waist packs out there that are built with lumbar panels in them for added back support which I really like as well.
Look Good: Totally subjective here, but I much prefer the look of a waist pack or sling. It just looks much more low-profile and lets people see that cool shirt you have on in full effect!