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You didn't specify how this new disk would be used, i.e. attached internally or via USB 3.0 (or 2.0) or even whether this was intended to be used as a source disk or destination disk. You also didn't provide any details about your outgoing disk other than its rotational speed, so answers here will necessarily be generalized. But the short and sweet answer is that in almost all cases, the write performance of the destination is the bottleneck when it comes to backups, so if this new disk is intended to replace your current source disk, it probably won't change anything. If it's a new destination disk and it's connected either internally or via USB 3.0, both of which have enough bandwidth to saturate a single spinning disk's capacity, then spinning disks can typically manage 70-120 MB/s. If you're upgrading from USB 2.0, then you should expect a drastic improvement, on the order of 3-5x -- but that's mostly because of USB 3.0, not your disk's rotational speed. If you were already on USB 3.0, you may see an improvement, but I wouldn't expect anything huge.
If you're interested in techy details, to expand on Froggie's answer a bit, it's relatively unlikely that your disks will have similar areal densities, and Froggie also didn't mention number of platters inside the drive as a factor. For example, you can build a 2TB drive out of 5x400GB platters or 4x500GB platters, or even 2x1TB platters these days. All else being equal, more platters means more throughput (and also more noise, power consumption, and heat). More areal density also means more throughput, which is why if you have a 2TB drive and a 3TB drive with the same number of platters, the 3TB drive may be faster. But notice that if you keep capacity constant, increasing platters (better performance) means reducing per-platter areal density (lower performance), so the net performance result of various design decisions isn't always obvious even if you have detailed specs of the drive's design.