Both controllers have their pros and cons.
Game Cube Controller Pros
The GCC has a button layout that works well in smash. The enlarged A button makes it easier to tell which button you are pressing and it is also easier to press the Y and A together for the short hop aerial shortcut. The octagonal ridges make diagonal inputs easier on both the control stick and the C-stick. I noticed that you put Pichu as your Ultimate main and lots of Pichu and Pikachu mains find it easier to get the Uspecial angles they want with the octagonal ridges. Being wired makes things simple as well since you don't have to sync it with new switches if you decide to go to tournaments. Wired controllers also don't suffer from interference (which is mostly a problem if you go to tournaments as well).
GCC Cons
The control stick and the buttons are pretty firm and take more effort to press than modern controllers. It isn't much, but over time it does wear on your hands. If you don't plan on playing 2 hours a day then I wouldn't worry about it (as an example my brother has used the GCC since melee and he hasn't had any finger strain) but hand strain has always been an issue with pro smash players. All of the shoulder buttons are terrible as well. The L and R buttons are analog and digital hybrid buttons but the switch only reads the digital inputs. This means that the switch only registers the input when the button is fully depressed so most of the motion used is wasted. This means that any action using those buttons will be slightly less responsive. The Z button is pretty bad as well. I've always found this button to be pretty awkward to press. It takes more force than is necessary and I don't like the shape or positioning. The controller can't really be used for anything but smash either so if you want to play other games and you don't want to buy two controllers the GCC won't help you there.
Pro Controller Pros
The PC fits much more comfortably in your hands than the GCC. The GCC was not designed very ergonomically so it always felt awkward in my hands. The buttons and control stick are responsive and don't require a lot of extra effort like the GCC. You can use it for other games so if you don't plan on buying another controller this can cover you there. The PC also has four shoulder buttons, as opposed to the GCC having three, and having that extra button is handy when you start customizing your button layout. The shoulder buttons are all digital so you don't have to waste most of your input like the GCC. You can also turn the Switch on with the wireless PC and that is pretty handy.
PC Cons
The standard button layout (the A, B, X, and Y buttons) isn't as smash friendly. This isn't a huge deal and it's easy to get used to the PC layout but that is something to keep in mind. The lack of octagonal ridges makes precise diagonal inputs harder and there are a lot of characters and techniques that will be either more difficult or more inconsistent to use. Pairing a wireless PC to a new switch is a pain if you go to tournaments and your input delay can be slightly affected by cell phone interference. I've never heard of an actual instance of this happening but it is possible. There is a wired version if that is a concern so you have that option as well.
Regarding input lag, I've read a lot and I've seen a lot of videos on the subject and every one has had slightly different conclusions. The bottom line is that most of the controllers aren't that much worse than each other if you are playing casually but there are differences. The wireless PC is the worst, the GCC is second and the wired PC is the best (because it doesn't have to connect to the adapter).
Hope this helps.