int i = new int();
is equavalent to
int i = 0;
There is no difference between them. They will generate the same IL code at all.
// Code size 4 (0x4)
.maxstack 1
.locals init ([0] int32 num)
IL_0000: nop
IL_0001: ldc.i4.0
IL_0002: stloc.0
IL_0003: ret
From Using Constructors (C# Programming Guide)
Constructors for struct types resemble class constructors, but structs cannot contain an explicit default constructor because one is provided automatically by the compiler. This constructor initializes each field in the struct to the default values.
Default value of integers is 0
. Check for more Default Values Table