I really like these types of questions, as you can do performance analysis.
First, let's create a sample database [test] with a table [urls] with a million random entries.
See the code below.
-- Switch databases USE [master]; go -- Create simple database CREATE DATABASE [test]; go -- Switch databases USE [test]; go -- Create simple table CREATE TABLE [urls] ( my_id INT IDENTITY(1, 1) PRIMARY KEY , my_link VARCHAR(255) , my_status VARCHAR(15) ); go -- http://stackoverflow.com/questions/1393951/what-is-the-best-way-to-create-and-populate-a-numbers-table -- Load table with 1M rows of data ; WITH PASS0 AS ( SELECT 1 AS C UNION ALL SELECT 1 ), --2 rows PASS1 AS ( SELECT 1 AS C FROM PASS0 AS A , PASS0 AS B ), --4 rows PASS2 AS ( SELECT 1 AS C FROM PASS1 AS A , PASS1 AS B ), --16 rows PASS3 AS ( SELECT 1 AS C FROM PASS2 AS A , PASS2 AS B ), --256 rows PASS4 AS ( SELECT 1 AS C FROM PASS3 AS A , PASS3 AS B ), --65536 rows PASS5 AS ( SELECT 1 AS C FROM PASS4 AS A , PASS4 AS B ), --4,294,967,296 rows TALLY AS ( SELECT ROW_NUMBER() OVER ( ORDER BY C ) AS Number FROM PASS5 ) INSERT INTO urls ( my_link , my_status ) SELECT -- top 10 search engines + me CASE ( Number % 11 ) WHEN 0 THEN 'www.ask.com' WHEN 1 THEN 'www.bing.com' WHEN 2 THEN 'www.duckduckgo.com' WHEN 3 THEN 'www.dogpile.com' WHEN 4 THEN 'www.webopedia.com' WHEN 5 THEN 'www.clusty.com' WHEN 6 THEN 'www.archive.org' WHEN 7 THEN 'www.mahalo.com' WHEN 8 THEN 'www.google.com' WHEN 9 THEN 'www.yahoo.com' ELSE 'www.craftydba.com' END AS my_link , -- ratings scale CASE ( Number % 5 ) WHEN 0 THEN 'poor' WHEN 1 THEN 'fair' WHEN 2 THEN 'good' WHEN 3 THEN 'very good' ELSE 'excellent' END AS my_status FROM TALLY AS T WHERE Number <= 1000000 go
Secondly, we always want to clear the buffers and cache when performing a performance analysis in our test environment. In addition, we want to include I / O statistics and time for comparing results.
See the code below.
-- Show time & i/o SET STATISTICS TIME ON SET STATISTICS IO ON GO -- Remove clean buffers & clear plan cache CHECKPOINT DBCC DROPCLEANBUFFERS DBCC FREEPROCCACHE GO
Third, we want to try the first TSQL statement. Look at the execution plan and write down the statistics.
-- Try 1 SELECT * FROM urls ORDER BY my_status /* Table 'urls'. Scan count 5, logical reads 4987, physical reads 1, read-ahead reads 4918, lob logical reads 0, lob physical reads 0, lob read-ahead reads 0. SQL Server Execution Times: CPU time = 3166 ms, elapsed time = 8130 ms. */

Fourth, we want to try the second TSQL statement. Remember to clear the query plan cache and buffers. If you do not, the request takes less than 1 second, since most of the information is in memory. Look at the execution plan and write down the statistics.
-- Try 2 SELECT ROW_NUMBER() OVER (ORDER BY my_status) as my_rownum, * FROM urls /* Table 'urls'. Scan count 5, logical reads 4987, physical reads 1, read-ahead reads 4918, lob logical reads 0, lob physical reads 0, lob read-ahead reads 0. SQL Server Execution Times: CPU time = 3276 ms, elapsed time = 8414 ms. */

And last but not least, here is the interesting part, performance analysis.
1 - We see that the background is a super-set of the first. In this way, both plans scan the clustered index and sort the data. Parallelism is used to combine results.
2 - The second plan / request should calculate the line number. It segments data and calculates this scalar. So we end up with two more operators in the plan.
It is not surprising that the first plan is executed in 8130 ms, and the second plan - 8414 ms.
Always look at the query plan. Both are priced and relevant. They say that you want the engine to plan and what it really does.
In this example, two different TSQL statements have almost the same plans.
Yours faithfully
John
www.craftydba.com