Compare / Join two object collections LINQ
This code seems to suffer from poor readability and maintainability. What does splitSmallLine[2] mean, and why do I care if it matches splitBigLine[1] (ponders the next developer to run into this code)? It's very easy to make mistakes in this code, so I think bringing some clarity into what you are actually selecting/comparing against will help.

Since I don't actually know what your files look like, or what the fields represent, let's just start here:

string[] small = new string[] {
    "Joe,Smith,22",
    "Sally,Jones,32"
};

string[] big = new string[] {
    "Smith,22,Joe",
    "Jones,34,Sally",
    "Doe,15,Jane"
};


We have two "files" that store people, but the fields aren't in the same place. The first thing you could do is bring meaning to your parsed rows, like so:

var smallFilePeople = from personLine in small
                      let personFields = personLine.Split(',')
                      select new
                      {
                          FirstName = personFields[0],
                          LastName = personFields[1],
                          Age = personFields[2]
                      };

var bigFilePeople = from personLine in big
                    let personFields = personLine.Split(',')
                    select new
                    {
                        FirstName = personFields[2],
                        LastName = personFields[0],
                        Age = personFields[1]
                    };


Now I know that I'm selecting people, and I have a single place to show what I'm actually pulling out of each indexed location. This makes writing a join query based on this very simple and easy to understand:

var joined = from smallFilePerson in smallFilePeople
             join bigFilePerson in bigFilePeople
                on new { smallFilePerson.FirstName, smallFilePerson.LastName } equals
                   new { bigFilePerson.FirstName, bigFilePerson.LastName }
             select new
             {
                 FirstName = smallFilePerson.FirstName,
                 LastName = smallFilePerson.LastName,
                 AgeInSmallFile = smallFilePerson.Age,
                 AgeInBigFile = bigFilePerson.Age
             };


This example is a bit more contrived than yours, but I'm sure you can see where this may help. I would also take this a step further and split out the query/parsing logic/joining into distinct functions. It's a good separation of concerns, and you may end up reusing the parsing for each file in other new ways.