These are the systems I have most experience running. In some ways they overlap, in others they’re complimentary opposites. I’m going to ruminate about my experience with each.
From a design perspective, ShadowDark asks, “What would DnD be like if BX adopted modern conventions?” Index Card RPG goes the other way, it asks, “What would it be like if 5e were streamlined?”
Kelsey Dionne and Hank Ferinale (Brandish Gillhelm, Runehammer) collaborate on projects. Kelsey contributed to the ICRPG Master Edition and she play tested Crown & Skull with Runehammer. Brandish made some art in ShadowDark, and is instrumental in creating the overall design of the book (which got it an Ennie). I would be surprised if he was not among the early play testers of the system.
So I find that thinking of the two is interesting. These are my ramblings about that.
Index Card RPG
ICRPG is a dice goblin’s dream. Tasks have HP and players attack the task, often in contention to a timer that makes the task urgent.
Long winded description
I found ICRPG because our noob table did not like our experience with 5e. Maybe it was me running my first game ever. I went hunting for something close to what I played in the late 80s. But really, I was looking for something more concise and easy to grasp. ICRPG fit the bill.
At a glance, it’s yet another 6-stat, d20, roll to hit, meet or beat the target system. It’s one of the early systems to diverge from 5e in 2016 to streamline the system.
Notably, stats are player chosen modifiers (distribute 6 points as you wish), it eschews XP, introduces an Effort system that uses d4 though d12 dice, and the target represents the environment instead of foes or challenges.
Target as Environment: it’s roll to hit. But everything in the scene uses the same target. If a scene’s target is 12 (normal) then everything must beat a 12 target. This applies to mooks, BBGs, picking a lock, whatever. If there’s a fog the target could be 16. A clear day could be 8.
A wizard can attack the target by clearing fog and drop the target to 12. Then a light spell is cast to improve visibility and the target becomes 9.
Also, attempting the exact same action twice reduces the target by -4. This represents learning from mistakes.
Great scenarios give players the means to attack the target. Attacking the target is a core player strategy.
Effort System: As a system, ICRPG is a dice goblin’s dream. Players can roll for just about everything. Instead of giving tasks a target to beat, they have HP to whittle away. So diffusing a bomb may have 10HP (1 
in ICRPG lingo).
The Effort system is fun and easy to remember. Manual tasks, like diffusing a bomb use d4. If you have a tool it’s a d6. If using the electrical schematics of the bomb, you roll with advantage (Big effort in ICRPG). A timer determines when the bomb will explode. The gamble, will you diffuse the bomb before it blows?, is exciting. The implication is that the system tends to use a lot of timers to create excitement and tension.
Monster difficulty is differentiated by their HP and GMs are encouraged to make them more dynamic instead of loading them up on HP.
No XP: progress is in milestones, classes only have three, the GM decides when characters advance.
As a result, ICRPG games tend to be very exciting with a lot of dice rolling. Players look for creative ways to improve their odds at a tasks.
ShadowDark
Is narrative driven and players just do what they know how to do. Rolling happens when there is risk in failure.
Long winded description
I found ShadowDark through a Discord message from Runehammer saying it was now available for general purchase. I grabbed it right way without knowing what I was getting into. Brandish Gillhelm has a bit of a cult of personality, I bought in. LOL 
ShadowDark is also a 6-stat, d20, roll to hit, meet or beat the target system. It is rooted in BX and the ethos that “combat is a failure state.” The GM is given a plethora of random tables to roll on and generate content.
ShadowDark is about the narrative. If you have the skill, you can. No roll needed. The challenge may be in getting into a position where the skill is used.
Targets (DC, Difficulty Class) change depending on what you are doing or what a foe’s AC is. The target represents difficulty of an action or defensive ability of a foe.
My typical ShadowDark games have very little dice rolling and focus heavily on players investigating and acting on what they learn. I generally roll more often than they do.
As a GM I’m often pulled between the dice heavy ICRPG and the narrative logic of ShadowDark. I’ve joked that I’d like to implement effort and the universal DC target in SD.
Using a d4 as a countdown to an event is a great way to create urgency and accelerate a slow moving game. Giving tasks HP provides resistance and uncertainty that pushes players to manipulate the environment in their favor. Planning for this encourages a scene based format I’ve moved away from.
ShadowDark’s narrative focus allows free-form exploration of a situation. The GM manages the big picture and describes how the environment responds. Rather than plan set-pieces, I expand and alter the world in response to player decisions.
In truth though, both systems use some kind of GM plan that responds to player choices. I appreciate running each on their own terms and borrowing strategies each other.
I find it’s most effective to use ShadowDark as a base. When needed I give a task HP and tell players the environment is affecting their ability to perform it. With this information and the tools available, players strategize how to improve their conditions or maximize the effect of their actions.