If you have a number of Canon fit lenses, the next step up would be a Canon 80D. Better AF for wildlife and very good image quality.
I don't get what you mean by "better shutter speed" though? Shutter speed is determined by your ISO and aperture. Do you mean either the speed that the camera focuses or the speed that the camera can take successive photos, ie the frames per second?
The 750D and 80D have the same number of megapixels on the sensor, but they're not quite the same.
The 750D goes 100-12800 ISO verses 100-16000 for the 80D. So the 80D will be better in lower light allowing you to have faster shutter speeds.
The 750D has 19 AF points, versus 45 for the 80D, meaning it can track moving wildlife/subjects better.
The 750D has a maximum shutter speed of 1/4000s, 80D = 1/8000s (this isn't a big problem though, some people rarely reach 1/4000th, you need very bright day for that)
The 750D does maximum of 5 frames per second, 80D = 7fps
The question is really in what way is your current camera not performing, have you reached the limit of what it can do?
Without trying to tempt you to spend more money, there's also the question of lenses. Lower budget lenses can sometimes be slower to focus (ie not helpful for fast moving subjects) and have higher minimum apertures (ie f5.6 is higher than f4) which means they don't let in as much light which means either your shutter speed needs to be a bit lower or your ISO needs to be higher to compensate.
It might be worth considering lenses before replacing the body.