So, I currently have a pretty old 8Gb SD-Card in my Moto G 2nd Gen Phone. Except photos, videos, and other miscellaneous files which can be easily transferred, I also have a lot of big apps. I did a bit of research and found that the data for these apps are stored in the folder Android_secure. I'm also aware that only the app's code and data that only need to be read and not modified stay there. Will just moving that folder (Android_secure) to the new SD work, or will there be any more complication? And no, I can't unfortunately move the apps to my phone, swap SDs and then move them to the new one. That's the reason the apps are in the SD in the first place, to free internal storage, so that I'm able to download more big apps to put in my SD card. Edit: My new SD-Card is a 32Gb if anyone cares.
As long as you are not on Marshmallow and are not using Adopted Storage, you can just copy all the data from one card to another.
I would suggest powering off and removing the card and inserting the new one, then powering up and formatting the new card, then power off and remove the card. In a computer with a card ready, copy all data from old card to the new card. Reinsert the new card in the phone and power up and you should be good to go.