I mine a bit more often as I prefer to gather tritium over buying it. It changed how I do commodity trading. Instead of A-B-A-B trade now its A-carrier, carrier-B, which as someone already pointed out opens up opportunities as every market in the Bubble is now one jump away.
If I may add, it also added a sort of economic strategy layer, as you can buy goods when they're at their lowest prices at any time and stash them until the time is right to sell them, obtaining maximum profit. You can also pre-purchase large quantities of certain goods, then jump to a system with fetch missions for those goods, as delivering goods through fetch missions is usually the highest profitable way. You can stash around some quantity of medicines, then drop them when some system goes into outbreak to take advantage of the medicines price bump.
Regarding mining, I started to keep every mineral worth more than 10K, instead of discarding everything except "X" like before. Then I stash everything in the FC, and just like trading, it's a matter of offloading all those minerals where and when the time is right. I use a Python for offloading mined minerals to avoid the bulk tax. Osmium for instance I never sell, I just wait until I see mining missions asking for osmium as these provide the best credits per ton, then I accept them all and deliver the osmium I already have onboard the carrier.
The FC cargo bay is an invaluable asset.
But to me where FCs are the biggest game changer is in exploration. Finally, like I always dreamed, I can finally explore the galaxy like a Captain Kirk.
The FC is my Enterprise, and a plethora of purpose built small ships are my shuttles. I use them as landing party shuttles, to explore systems, prospect rings, investigate phenomena, and explore the general area around the FC. None of them have fuel scoops (but a couple have an extra fuel tanks) to give me that "running low on fuel - returning to base" role-play feeling. Aside from small ships, I only take an exploration built T-7, fully autonomous. It's my long-range science ship for venturing far from the FC whenever necessary. And a T-10 miner, which I use during the trip when I find worthy rings, to fund the next expedition. Other ships stay back home.