Description of Serpent
I'd suggest you read the paper submitted during the AES contest:
Serpent is slower than Rijndael (cipher chosen to become AES), because it uses more rounds. See these benchmarks, Serpent in CTR mode could encrypt 32 MiB/sec while AES-256 in CTR mode could encrypt 96 MiB/sec. Additionally Serpent took 1.2 microseconds to setup key and IV while AES-256 took 0.76 microseconds. More benchmarks from the AES contest are available here; on a variety of platforms Serpent can encrypt 2 to 4 times less data than Rjindael (granted this was Rjindael which was slightly tweaked to become AES).
Roughly equal in that both when implemented properly are secure against all known computationally feasible attacks. There are slightly better attacks on AES, but all the public attacks on AES are not computationally feasible (e.g., 4 times faster than brute-force) as well as other obscure attacks on AES (that is there's a related-key attack on AES that assuming some strange conditions is significantly better than brute force but is irrelevant for AES as typically used in a way susceptible to the attack, and then even then the best related-key attack takes 299.5 time which is not feasible). A large reason for more attacks on AES is that AES is widely used and analyzed, Serpent is not used nearly as much as it didn't win the AES competition (Rijndael won and became AES).
Mode of Operation
The mode of the operation is independent of the block cipher used--it's a separate choice. That is you can use either serpent or AES or any other block cipher in any block cipher modes. A mode of operation just considers how you take a block cipher that can only be used to encrypt/decrypt blocks of a fixed size (e.g., 128-bit block for Serpent256 and AES256 - the 256-bit stands for the keysize) and use it to encrypt/decrypt arbitrarily sized blocks of text without potentially leaking information if your plaintext is redundant (except in ECB mode which is an insecure mode where you naively just split the plaintext into equal sized blocks and apply the block cipher on each block independently).