Does large VARCHAR take up more room in the transaction log On SQL Server, would VARCHAR(500) take up more space in the transaction log than VARCHAR(100) when all the rows have no more than 100 characters?
In the case of a small insert, there is no difference in size of transaction log generated.

Here's a demo script to prove it (SQL Server 2016):

--setup
USE master
GO
CREATE DATABASE LogTest
GO
ALTER DATABASE LogTest
SET RECOVERY SIMPLE
GO
USE LogTest
GO

CREATE TABLE dbo.v100 (junk VARCHAR(100) )

CREATE TABLE dbo.v8000 (junk VARCHAR(8000) )
GO

--initial inserts have extra log activity from initializing the table
INSERT dbo.v100
VALUES ('z')

INSERT dbo.v8000
VALUES ('z')

-----------------------------------------------------------------
--ok, let's test this
CHECKPOINT --checkpoint clears log in SIMPLE recovery, which helps limit it to what we want to see
GO

BEGIN TRAN
INSERT dbo.v100
VALUES ('a')
ROLLBACK

SELECT Operation, Context, [Log Record Length], [Log Reserve]
FROM sys.fn_dblog(NULL,NULL)
WHERE Operation NOT LIKE '%CKPT'

CHECKPOINT
GO

BEGIN TRAN
INSERT dbo.v8000
VALUES ('a')
ROLLBACK

SELECT Operation, Context, [Log Record Length], [Log Reserve]
FROM sys.fn_dblog(NULL,NULL)
WHERE Operation NOT LIKE '%CKPT'