So each image you upload to the site is built in with a border around it, so you can see it was sliced in half to make it fit? I've seen that on some websites before.
You have a few options it sounds like, one is make smaller upload chapters. Or upload images that slice at the panel line horizontally. It does mean re-slicing a looooot of pages for just one site. For me, it's not worth the work unless you find it somehow calming. If you do, I'd suggest doing it in batches: 1hr every few days when you're bored or feel like it. If you try to do it all at once, you'll be mad you have to do it.
For other's images looking good I'm not sure. I don't frequent either site often but I know from deviantART that for a while if I uploaded an image in jpeg, not png, it'd compress the image and make it look horrible. But it would be unable to compress the png without entirely re-saving it as a jpg (requires the site to do more work, so it doesn't). If the site allows, try uploading in png instead and see if you still have the issue for compression. Most files jpeg/png sizes are similar until you get to really large sizes / transparency. Save a png without transparency, and it should be similar size to a jpeg, though it can be double.
Of that note, sometimes re-saving an image is the way to go. So do you art in one program, let's say SAI, and you save as no transparency png. It flattens the image. Close the program and everything, then re-open and open that png you just saved. Now resave it as png, and ideally the file will be smaller- though sometimes it can be larger. Sometimes if you open in another program it'll change too - so open it in Photoshop and save as png and it'll be smaller.
Programs are weird from a tech standpoint - addresses and things being put into the code of the image can make the file size larger, or which program is saving it. SAI can save better quality jpeg than Paint.NET's freeware, for example. Even though both have the ability to scale the compression percentage. No two programs are alike!
Another tip is save in your art program so it flattens the image. make sure it's no transparency. Then open that image and slice off a few pixels and save it again, and it might be smaller. But since it doesn't have to run through the code of "flatten" it, it can skip that step and that saves on the code to make the file. Lots of weird things will adjust filesize.
Compression is harder because it might be out of your control. If it's just you uploading jpeg to their site at a certain pixel size to avoid it being resized smaller, then fantastic. You just need to find the sweet spot. If the site is like tumblr and compresses based on file size AND pixel size, then you're out of luck. I get the feeling wattpad specifically works with compressing everything it can and is very pixel sensitive to the few times I've used it and had to upload images for a cover on there.
