Many shared web hosts like to advertise their server hardware, and the most popular thing to brag about these days is the brand of CPU used. Nearly all web hosts use processors made by AMD or Intel. Does it matter which one your host prefers? Is one faster over the other?
In short, it isn’t important what brand processor your host chooses. While one particular processor model might be faster than another, the more important factor is how heavily loaded a provider’s servers are. Will you be sharing a server with 10 other customers, 100, or 1,000?
A web host can adjust the number of customers on a server to fit its speed, but if your host is overcrowding to save money, processor speed becomes irreverent. See if past customers have had problems with overloaded servers by searching the web for reviews.
If you plan on renting a VPS or dedicated server, processor brand shouldn’t be an issue as well, but you will want to compare models for differences in speed. For this, I recommend the CPU benchmarks at Tom’s Hardware.