A long time ago AMD was Intel's biggest rival but in more recent times this is no longer the case. It's been a long time since AMD has been able to compete with Intel in terms of raw CPU performance, and with the shift towards more portable computing devices, the biggest threat to Intel is not coming from AMD but from ARM. According to FUD Zilla, the chip giant now sees Qualcomm as its biggest competitor.
Qualcomm has swept across the US smartphone market due to its dominance with LTE integrated SOC and Intel and Nvidia want a piece of that market. Right now AMD looks quite weak in its eternal fight against Intel and the Core architecture dominates the PC and especially notebook market, the fight goes down to tablets and phones.
Intel wants to get into many Windows 8 and eventually Android tablets as well as phones. Qualcomm is in the way and it currently looks really strong in these markets. The key to success is LTE as well as low power chips and Intel is getting better and better in this market with each generation.