I just started with a volunteer fire department over the summer. Every Tuesday we go through 1-2 of our apparatus (ambulance, fire truck, water tender, or brush truck) and inventory everything. A few weeks ago we were doing medical scenarios in training and started an IV on the patient. We were using the kit from our primary ambulance. When the EMT pulled the IV out she couldn't get the bleeding contained with just the 2x2" gauze she had and frantically the other two first responders went through every pouch on the bag trying to find some 4x4" pads. They finally found one after about two minutes (which felt like five minutes with someone bleeding in front of you onto the firehouse carpet).
There were two morals to this story to me. The first is that whoever did the last inventory was in such a routine of checking expiration dates in the drug kits that they skipped over some of the very most basic items needed in emergency first aid. The second is that more pockets don't make a kit more effective.
Here's my car first aid kit. It's over 15 years old and evolved out of the kit I used to carry on ATVs while working for the forest service (same bag, mostly the same contents). 70% of the time it gets used it's for a mountain biking buddy who earned himself a twisted ankle, some road rash, or a small laceration; 20% of the time it's my wife or I have a headache or a cut finger, 10% of the time it's a serious motor vehicle accident. The kit needs to be adequate for all those possibilities.
Unzipped top view. On the outside pouch on the left is my pocket mask, on the outside pouch on the right is my gloves. There's several bottles, starting at the left: Sterile saline solution (for cleaning wounds), asthma rescue inhaler (probably so expired it should be tossed), Betadine, and hydrogen peroxide. There's also a 6" IBD, 3" Ace bandage, 1.5" cloth tape, Instant ice pack, and 4" kerlix roll. Everything else is in ziplock bags which I'll show open below, individually:
General purpose bag: Emergen-C packets, Tums, Immodium, lighter, suction bulb, pseudofed, flashlight with spare batteries, sharpie, OTC med bottle, GasX, Peptobismo, Q-tips in long bottle, Antihistamine tablets, 3 days prescriptions, straight and curved clamps (not sure why I have them in there).
Small to medium dressings: Bandaids, non-stick dressings, moleskin, steristrips, gauzes and sponges up to 4x4"
Large dressings & blood stoppers (6x6" & 5x9")
Not previously mentioned: Large space blanket in back of pack, 2nd flashlight. Might consider adding a headlamp or headband to hold flashlight.
In any case, I'm a fan of clear ziplocks so you can see what is inside, group similar items together, and sort through what you do and don't need quickly. More pockets to me just add time to accessing what you need. If you used the kit every day, you might know exactly where everything is when you needed it, but even with guys what have been with my department for several years and gone on dozens of calls (we're a small department and get between 75-125 calls a year), they still couldn't find what they needed in a hurry.
At home I have a small rubbermaid tub (maybe two gallons?). It's mostly different sizes of bandaids, pain relievers, tweezers, bandage scissors, and a couple items for serious situations (epi-pen, IBDs and a tourniquet). I keep two or three 1 quart seal-a-meal bags filled with corn syrup in my freezer for cold packs (they're awesome because they're cheap, last forever, and conform to your injured part). I also have a blowout kit in my gun bag that contains the essentials to deal with a gunshot wound. Otherwise most of my stuff is several large rubbermaid bins downstairs. I don't need to be able to readily access a lot of the stuff I stock in a hurry; control bleeding and the rest can wait.