Here are some utility functions that allow you to determine if two files (or two streams) contain identical data.

I have provided a "fast" version that is multi-threaded as it compares byte arrays (each buffer filled from what's been read in each file) in different threads using Tasks.

As expected, it's much faster (around 3x faster) but it consumes more CPU (because it's multi threaded) and more memory (because it needs two byte array buffers per comparison thread).

    public static bool AreFilesIdenticalFast(string path1, string path2)
    {
        return AreFilesIdentical(path1, path2, AreStreamsIdenticalFast);
    }

    public static bool AreFilesIdentical(string path1, string path2)
    {
        return AreFilesIdentical(path1, path2, AreStreamsIdentical);
    }

    public static bool AreFilesIdentical(string path1, string path2, Func<Stream, Stream, bool> areStreamsIdentical)
    {
        if (path1 == null)
            throw new ArgumentNullException(nameof(path1));

        if (path2 == null)
            throw new ArgumentNullException(nameof(path2));

        if (areStreamsIdentical == null)
            throw new ArgumentNullException(nameof(path2));

        if (!File.Exists(path1) || !File.Exists(path2))
            return false;

        using (var thisFile = new FileStream(path1, FileMode.Open, FileAccess.Read, FileShare.ReadWrite))
        {
            using (var valueFile = new FileStream(path2, FileMode.Open, FileAccess.Read, FileShare.ReadWrite))
            {
                if (valueFile.Length != thisFile.Length)
                    return false;

                if (!areStreamsIdentical(thisFile, valueFile))
                    return false;
            }
        }
        return true;
    }

    public static bool AreStreamsIdenticalFast(Stream stream1, Stream stream2)
    {
        if (stream1 == null)
            throw new ArgumentNullException(nameof(stream1));

        if (stream2 == null)
            throw new ArgumentNullException(nameof(stream2));

        const int bufsize = 80000; // 80000 is below LOH (85000)

        var tasks = new List<Task<bool>>();
        do
        {
            // consumes more memory (two buffers for each tasks)
            var buffer1 = new byte[bufsize];
            var buffer2 = new byte[bufsize];

            int read1 = stream1.Read(buffer1, 0, buffer1.Length);
            if (read1 == 0)
            {
                int read3 = stream2.Read(buffer2, 0, 1);
                if (read3 != 0) // not eof
                    return false;

                break;
            }

            // both stream read could return different counts
            int read2 = 0;
            do
            {
                int read3 = stream2.Read(buffer2, read2, read1 - read2);
                if (read3 == 0)
                    return false;

                read2 += read3;
            }
            while (read2 < read1);

            // consumes more cpu
            var task = Task.Run(() =>
            {
                return IsSame(buffer1, buffer2);
            });
            tasks.Add(task);
        }
        while (true);

        Task.WaitAll(tasks.ToArray());
        return !tasks.Any(t => !t.Result);
    }

    public static bool AreStreamsIdentical(Stream stream1, Stream stream2)
    {
        if (stream1 == null)
            throw new ArgumentNullException(nameof(stream1));

        if (stream2 == null)
            throw new ArgumentNullException(nameof(stream2));

        const int bufsize = 80000; // 80000 is below LOH (85000)
        var buffer1 = new byte[bufsize];
        var buffer2 = new byte[bufsize];

        var tasks = new List<Task<bool>>();
        do
        {
            int read1 = stream1.Read(buffer1, 0, buffer1.Length);
            if (read1 == 0)
                return stream2.Read(buffer2, 0, 1) == 0; // check not eof

            // both stream read could return different counts
            int read2 = 0;
            do
            {
                int read3 = stream2.Read(buffer2, read2, read1 - read2);
                if (read3 == 0)
                    return false;

                read2 += read3;
            }
            while (read2 < read1);

            if (!IsSame(buffer1, buffer2))
                return false;
        }
        while (true);
    }

    public static bool IsSame(byte[] bytes1, byte[] bytes2)
    {
        if (bytes1 == null)
            throw new ArgumentNullException(nameof(bytes1));

        if (bytes2 == null)
            throw new ArgumentNullException(nameof(bytes2));

        if (bytes1.Length != bytes2.Length)
            return false;

        for (int i = 0; i < bytes1.Length; i++)
        {
            if (bytes1[i] != bytes2[i])
                return false;
        }
        return true;
    }