is the default ore any easier to find than it's alternate?

Solution 1:

Platinum is an alternative ore to gold, even though the items made from it are slightly better. As far as rarity, it is the same as gold and can be found in the same places.

I have noticed in worlds where platinum exists, I may overlook it thinking that it is either stone or silver. This is especially true when I'm not actively looking for the Tier 3/4 ores. On the other hand, gold stands out like a sore thumb and therefore is easier to accumulate when I'm not specifically looking to craft T4 items.

If you're interested in how ores are generated, we can investigate the source code. Line 3456 defines the following function:

public static void generateWorld(int seed = -1)

We're interested in the following bit:

int type = 7;
int type2 = 6;
int type3 = 9;
int type4 = 8;
Main.cloudBGActive = (float)(-(float)WorldGen.genRand.Next(8640, 86400));
WorldGen.copperBar = 20;
WorldGen.ironBar = 22;
WorldGen.silverBar = 21;
WorldGen.goldBar = 19;
if (WorldGen.genRand.Next(2) == 0)
{
    type = 166;
    WorldGen.copperBar = 703;
}
if (WorldGen.genRand.Next(2) == 0)
{
    type2 = 167;
    WorldGen.ironBar = 704;
}
if (WorldGen.genRand.Next(2) == 0)
{
    type3 = 168;
    WorldGen.silverBar = 705;
}
if (WorldGen.genRand.Next(2) == 0)
{
    type4 = 169;
    WorldGen.goldBar = 706;
}

For reference, here are the related tile ID's used in the above snippet:

public const ushort Iron = 6;
public const ushort Copper = 7;
public const ushort Gold = 8;
public const ushort Silver = 9;

public const ushort Tin = 166;
public const ushort Lead = 167;
public const ushort Tungsten = 168;
public const ushort Platinum = 169;

The bars are item IDs, not tile IDs, here are the related item IDs:

public const short GoldBar = 19;
public const short CopperBar = 20;
public const short SilverBar = 21;
public const short IronBar = 22;

public const short TinBar = 703;
public const short LeadBar = 704;
public const short TungstenBar = 705;
public const short PlatinumBar = 706;

As you can see from the source code, the alternative ores are determined ahead of the actual generation. The generation algorithm isn't even aware of the difference between the two different types of ores in each tier since it is simply fed the IDs directly. Therefore there is literally no difference between alternative ores in the same tier as far as where you can find them, how rare they are, etc...