The velcro and cards seem like the best option for me.
Unless you have one of those old top folding stocks...

The hard receiver mounted options are heavier and relatively fixed (tools and various replacement pins mean taking it off is a chore). And if the shell holding loops loosen up or break, the whole thing is trash.

Advantage of the cards, other than simple removal if needed, is that you can carry ammo in extra cards, full with various ammo types, and just slap a full one on the velcro whenever needed.
Also, a velcro strip can be added to the stock (in addition to the receiver) if you want to carry 2 cards.

 

I have probably gone through most of the ways to carry extra shells out there over the decades and I have found that the Velcro shell cards are the way to go, for all the reasons that 311INF mentioned above.

 

My older shotguns have the bolt-on Tacstar-brand 4-round sidesaddles with a 5 or 6 round on the butt-stock. See:

SideSaddles | TacStar Accessories

Shop our selection for convenient and accessible sidesaddles for fast reloading. Shop TacStar today!

www.lymanproducts.com

PHOENIX TECHNOLOGY, LTD SHOT SHELL CARRIER | Brownells

Shell carrier attaches to buttstock and provides quick, convenient access to five additional shells for competition, sporting clays, or hunting. Attaches to most synthetic or wooden stocks. Mounting hardware and template included. Requires drillin...

www.brownells.com

My later shotgun has 5-round ESSTAC velcro carriers:

Shop All - Shotgun - Esstac

esstac.com

At the time, I liked the 4-round Tacstar side-saddles as it left enough room when I used the pump/slide to keep my left hand from bumping into the shell carrier. I did try a 6-round initially but gave it away as my left hand just didn't clear that carrier too well. Overtime, I have lost a screw which held the polymer carrier to the aluminum backing plate; and eventually, even with Loctite, the screws might loosen over time (I've had these Tacstars on for ~20 years now). Generally, they've worked well for me.

On the buttstocks of the older guns, I also have the screw-on 5-round no-name shell carriers. These required drilling into the stock and securing with self-tapping screws. The polymer on these are more flexible/softer than the tacstar polymer. Eventually, maybe ~5 years, the polymer will crack or rip and these shell-carriers will need replacement. For these, next time I'll go with the hook & loop (aka Velcro) type.

Esstac. There is another brand which I hear are also good. I've just not tried this other browncoattactical.com brand:

https://www.browncoattactical.com

With these Velcro type, they work very well. I have had the Velcro (bought separately) sometimes not stick completely well on my buttstocks, but I may just need to clean the buttstock better and try a new piece and try again. I bought 5-round cards which worked well size-wise on the receiver and the buttstock.

What didn't work well were inexpensive shell cards bought on Amazon, made in China. The elastic loops were just to weak to adequately hold the shot shells. Amazon has these under several different brand names.

BTW, I've got one 11-87P, Remington; two 870 Remingtons; and one 590A1 Mossberg.

I've also tried and use some other nylon buttstock shell carriers but I can't remember the brand right now (unknown if they're still in business).

Edit to add: SpecterGear is the brand. The straps can be a bit annoying, but these carriers also work ok:

Buttstock Shotshell Holders

Specter Gear is known for many fine products, but what we're best known for is our tactical slings. It's what started our company in 2000 and remains a core product line for us. We currently have the most comprehensive selection of Tactical Slings in the industry with a stellar reputation for...

www.spectergear.com

 

There is another brand which I hear are also good. I've just not tried this other browncoattactical.com brand:

https://www.browncoattactical.com

With these Velcro type, they work very well. I have had the Velcro (bought separately) sometimes not stick completely well on my buttstocks, but I may just need to clean the buttstock better and try a new piece and try again. I bought 5-round cards which worked well size-wise on the receiver and the buttstock.

I've had 2 of these on my 20 gauges for about 3 yrs and have had no problems

 

I’ve got a Mesa Tactical aluminum shell carrier on my M4-it appears to be a high-quality, well-built and durable carrier, but it holds the shells so tightly that it is VERY difficult to remove them. I’ve left some snap caps in the holes in hopes of loosening up the rubber tube that provides the retention, but so far it hasn’t helped.

I’m going to wait a little while longer to see if it loosens up some but if not, I’ll be going the EssTac shell card route.

 

I had one on an Ithaca riot shotgun once. It worked well for the bottom loader.

 

I've been using Tac-Star plastic side saddles for decades. I've also used nylon/elastic butt cuff carriers. The elastic weakens in about five years in my experience so I haven't used the elastic card type carriers yet. YMMV. tom.

 

I'm on the card side of the fence.

 

Shotgun cards usually fit in M4gery mag shingles.

 

Esstac is the brand I've purchased also. They are pretty inexpensive and come in various sizes and patterns. Here's the 6 shell card in OD green.

I've found that the loops hold tightly but not too much for quick removal.

 

Esstac is the brand I've purchased also. They are pretty inexpensive and come in various sizes and patterns. Here's the 6 shell card in OD green.
View attachment 980151

I've found that the loops hold tightly but not too much for quick removal.

That's the brand I would consider when these Tac-Star units fail. tom.

 

I‘ve had the same six round side saddle bolted onto my 14” 870 for probably 20 years now. I like it and don’t see a need to change. I keep three Brenneke slugs and three Federal nine pellet 00 buck in it. Was perfect for work. I can see why folks might like the card thing, though.