Neither is correct. Int is an alias for a type, Int32 on 32-bit systems, Int64 on 64-bit systems. The method of float you invoke forwards to AbstractFloat, whose methods are mostly implemented to forward to Float64, but that’s not a guarantee for all possible methods e.g. AbstractFloat(big(1)). Moreover, the float function has other methods that don’t return an AbstractFloat type, e.g. float(1:5). It’s not a type constructor.
Int and float are thus not analogous functions. Often if you wanted to convert a non-integer type to an integer you would need to do something such as round(Int, x).
int-ifying runs into rounding or magnitude issues far more easily, and there’s no convenient default way to handle those, so might as well manually do it with a bunch of other functions and arguments.