The Star Trek Fact Files that I collected as a kid say that the Enterprise NCC1701 in the original timeline was a Heavy Cruiser, as more advanced ships (Excelsior) were built it was then demoted to a Light Cruiser.
The class of a ship depends on many things such as its size, offensive armament and defensive capabilities compared to other ships of the same reality and time period.
So my guess is that the NuEnterprise is a Heavy Cruiser like before, at least until the Excelsior is properly introduced, the Kelvin was probably a light cruiser based on its reduced armament rather than its size.
I can probably scan the ship sheets from the fact files if anyone is interested. I've got the plans and everything.