Realistically, the only difference between the classes of freighter is space. More inventory space and more tech space without having to do derelicts to get upgrades - and those only got patched in recently, before then the amount of space any freighter had was what you were stuck with.
In practice you’re not going to be filling the tech spaces until VERY late in the game anyway, so that’s kind of irrelevant. But more inventory space is a very nice ‘quality of life’ feature once you start having multiple frigate missions reporting in simultaneously - the limit on the cargo you can reclaim is the number of slots in your freighter inventory. OK, so if you fill up the inventory slots in your freighter you just have to manage/store it all elsewhere then go back and unload the remaining frigate missions once you’ve got space to, but being able to do them all at once then just deal with one ‘set’ of the results is actually quite a time saver.
You can probably cope with a ‘c’ class with like 9 or 10 free slots for a while, but once you start getting a significant frigate fleet together you will probably need to upgrade - and that then requires you to rebuild your ‘on freighter base’ (and you don’t get all the resources you used building the old one back) so it can be a bit of a hassle to upgrade. Not horrible, but more stuff to do. You may view that as a good thing…
The catch is freighters are one of the better ways to the earn cash & resources you need to progress through the game, so if you don’t have one, you’re going to be making slower going for the period while you’re jumping around trying to run into the A class mission. Basically you’re sticking in the early game longer to speed up the mid game, and that’s a choice that’s basically preference.