Is ROLLBACK a fast operation? Is it true that RDBMS systems are optimized for COMMIT operations? How much slower/faster are ROLLBACK operations and why?
For SQL Server, you could argue that a commit operation is nothing more than writing LOP_COMMIT_XACT to the log file and releasing locks, which is of course going to be faster than the ROLLBACK of every action your transaction performed since BEGIN TRAN.

If you are considering every action of a transaction, not just the commit, I'd still argue your statement is not true. Excluding external factors, speed of log disk compared to data disk speed for example, it's likely the rollback of any work done by a transaction will be faster than doing the work in the first place.

A rollback is reading a sequential file of changes and applying them to in-memory data pages. The original "work" had to generate an execution plan, acquire pages, join rows etc.

Edit: The it depends bit...

@JackDouglas pointed to this article which describes one of the situations where rollback can take significantly longer than the original operation. The example being a 14 hour transaction, inevitably using parallelism, that takes 48+ hours to rollback because rollback is mostly single threaded. You would most likely also be churning the buffer pool repeatedly, so no longer are you reversing changes to in-memory pages.

So, a revised version of my earlier answer. How much slower is rollback? All other things considered, for a typical OLTP transaction it isn't. Outside the bounds of typical, it can take longer to "undo" than "do" but (is this a potential tongue twister?) why will depend on how the "do" was done.

Edit2: Following on from discussion in the comments, here is a very contrived example to demonstrate that the work being done is the major factor in determining the relative expense of commit vs rollback as operations. 

Create two tables and pack them inefficiently (wasted space per page):

SET STATISTICS IO OFF;
SET STATISTICS TIME OFF;
SET NOCOUNT ON;
GO

CREATE TABLE dbo.Foo
(
    col1 INT IDENTITY(1,1) PRIMARY KEY CLUSTERED
    , col2 CHAR(4000) NOT NULL DEFAULT REPLICATE('A', 4000)
)

CREATE TABLE dbo.Bar
(
    col1 INT IDENTITY(1,1) PRIMARY KEY CLUSTERED
    , col2 CHAR(4000) NOT NULL DEFAULT REPLICATE('A', 4000)
)
GO

INSERT dbo.Foo DEFAULT VALUES
GO 100000

INSERT dbo.Bar DEFAULT VALUES
GO 100000


Run a "bad" update query, measuring time taken to do work and the time taken to issue the commit.

DECLARE 
    @StartTime DATETIME2
    , @Rows INT

SET @Rows = 1

CHECKPOINT
DBCC DROPCLEANBUFFERS

BEGIN TRANSACTION

SET @StartTime = SYSDATETIME()

UPDATE
    dbo.bar
SET
    col2 = REPLICATE('B', 4000)
FROM
    dbo.bar b
INNER JOIN
    (
    SELECT TOP(@Rows)
        col1
    FROM
        dbo.foo
    ORDER BY
        NEWID()
    ) f
ON  f.col1 = b.col1
OPTION (MAXDOP 1)

SELECT 'Find and update row', DATEDIFF(ms, @StartTime, SYSDATETIME())

SET @StartTime = SYSDATETIME()

COMMIT TRANSACTION

SELECT 'Commit', DATEDIFF(ms, @StartTime, SYSDATETIME())
GO


Do the same again but issue and measure rollback.

    DECLARE 
    @StartTime DATETIME2
    , @Rows INT

SET @Rows = 1

CHECKPOINT
DBCC DROPCLEANBUFFERS

BEGIN TRANSACTION

SET @StartTime = SYSDATETIME()

UPDATE
    dbo.bar
SET
    col2 = REPLICATE('B', 4000)
FROM
    dbo.bar b
INNER JOIN
    (
    SELECT TOP(@Rows)
        col1
    FROM
        dbo.foo
    ORDER BY
        NEWID()
    ) f
ON  f.col1 = b.col1
OPTION (MAXDOP 1)

SELECT 'Find and update row', DATEDIFF(ms, @StartTime, SYSDATETIME())

SET @StartTime = SYSDATETIME()

ROLLBACK TRANSACTION

SELECT 'Rollback', DATEDIFF(ms, @StartTime, SYSDATETIME())
GO


With @Rows=1 I get a reasonably consistent:


5500ms for the find/update
3ms commit
1ms rollback


With @Rows=100:


8500ms find/update
15ms commit
15ms rollback


With @Rows=1000:


15000ms find/update
10ms commit
500ms rollback


Back to the original question. If you're measuring time taken to do work plus the commit, rollback is winning hands down because the majority of that work is spent finding the row to update, not actually modifying data. If you're looking at the commit operation in isolation, it should be clear that commit does very little "work" as such. Commit is "I'm done".