Neither 3DES or 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 264/2 blocks, i.e. 32 gigabytes; AES uses 128-bit blocks, for a limit of 2128/2 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.