You missed a chance to save money and get a Crop Camera like the 70D instead of the 300mm f4.A 70-200/2.8 on a crop body is still a 70-200/2.8. However, if you want to look at it in 35mm terms, equivalence isn't just something restricted to focal length - it effects equivalent aperture and ISO too. The only part which needs no equivalence when comparing different sensor sizes is shutter speed.
Together with the 70-200mm 2.8 II you'd have the same amount of reach, you'd be more flexible and have one f-stop more speed.
A 70-200 used on a crop camera at 187.5mm, f2.8, ISO 10000 is the equivalent of 300mm, f4.5, ISO 25600 on FF - equivalent in terms of AoV, DoF and S/N ratio (focal length x 1.6, aperture x 1.6, ISO x 1.6^2). And if you use the same shutter speed on both, the exposure will be the same too.
If the 70-200 on crop was really the direct equivalent of FF 112-320/2.8, who'd ever buy a 1D X and 300/2.8 combo? Or use a m43's camera for a so called 140-400/2.8 - if so, what's the point in the big, heavy, expensive and 'slow' 200-400/4? And why not mount a 70-200/2.8 on a Pentax Q for a 5.64x crop, giving what could erroneously be called a 395-1128/2.8 lens? What were Canon doing with the 1200/5.6 when all they needed to do was make tiny sensors or use tiny film instead?