Security comparsion of 3DES and AES

Go for AES.

AES is the successor of DES as standard symmetric encryption algorithm for US federal organizations. AES uses keys of 128, 192 or 256 bits, although, 128 bit keys provide sufficient strength today. It uses 128 bit blocks, and is efficient in both software and hardware implementations. It was selected through an open competition involving hundreds of cryptographers during several years.

DES is the previous "data encryption standard" from the seventies. Its key size is too short for proper security. The 56 effective bits can be brute-forced, and that has been done more than ten years ago. DES uses 64 bit blocks, which poses some potential issues when encrypting several gigabytes of data with the same key.

3DES is a way to reuse DES implementations, by chaining three instances of DES with different keys. 3DES is believed to still be secure because it requires 2¹¹² operations which is not achievable with foreseeable technology. 3DES is very slow especially in software implementations because DES was designed for performance in hardware.

Resources:
http://www.differencebetween.net/technology/difference-between-aes-and-3des http://www.icommcorp.com/downloads/Comparison%20AES%20vs%203DES.pdf (offline, still in the Web Archive)

Neither 3DES nor AES is breakable with current technology (and foreseeable technology as well). However, you may encounter some security issues with 3DES if you encrypt more than about 32 gigabytes of data with a single key, whereas the limit is much higher with AES (this is due to the block size; 3DES uses 64-bit blocks, which can lead to trouble after processing 2^64/2 blocks, i.e. 32 gigabytes; AES uses 128-bit blocks, for a limit of 2^128/2 blocks, i.e. 2⁶⁸ bytes, also known as "quite a lot of data").

Since AES is also noticeably faster than 3DES, there is little reason to use 3DES for new designs.