Speed of Searching Text vs INT/BIGINT - SQL Server 2012
As other suggested, sometimes the best choice is to test it out yourself. I hate answering my own question, so if someone can provide a better answer then I might chose it if it better explains my results. 

It turns out there is not UBIGINT64 in SQL, so I created the table as I described as follows and used decimal instead of BigInt:

CREATE TABLE [dbo].[KEYS](
    [id] [int] IDENTITY(1,1) NOT NULL,
    [KEY] [nvarchar](max) NOT NULL,
    [BI1] [decimal](28, 0) NOT NULL,
    [BI2] [decimal](28, 0) NOT NULL,
    [i1] [int] NOT NULL,
    [i2] [int] NOT NULL,
    [i3] [int] NOT NULL,
    [i4] [int] NOT NULL
) ON [PRIMARY] TEXTIMAGE_ON [PRIMARY]


I then wrote a script to populate the table with approximately 2.25 million rows of data and setup the following loop to see how long each one would take.

declare @x integer
set @x = 0
while @x &lt; 100
begin
    --QUERIES WERE INSERTED HERE
    set @x = @x + 1
end


I then plugged the following three queries into the loop and recorded the results for 50 loops and 100 loops.

select * from IntTypes where i1 = 64003101 and i2 = 64003107 and i3 = 64003144 and i4 = 640031031



50 Loops: 9 seconds
100 Loops: 18 seconds

select * from IntTypes where BI1 = 15284527576400310788 and BI2 = 16825458760271544958



50 Loops: 11 seconds
100 Loops: 23 seconds

select * from IntTypes where [KEY] = 'a123f-5n12d1km9-3cmc32mc32-32cm0429c-243g4453-g43f43'



50 Loops: 54 seconds
100 Loops: 1 minute 48 seconds

Perhaps the results would be different if I did use a BIGINT instead of a DECIMAL, but comparing 4 integer columns seems to outperform comparing the two decimal columns. Both of those completely destroyed the text search results timing, but overall it looks like I will be using integer columns. 

So to sum it up and answer my own question (sort of), it is faster to search 4 integer columns than searching two decimal columns.