The main difference between the two CPU manufacturers is the price.
In the latest upgrade of CPU's in the CPU war, Intel first came out with the i7 CPU, but as only the people buying an i7 based system were the type of people who had a lot of money to spend, or the people who just HAVE to have the 'latest, and greatest' Intel, came out with a more economical i5 CPU, and then as the i5 didn't go as good as they thought, they then came out with the i3. AMD on the other hand didn't have to make cheaper versions in order to sell their product.
There are other things also such as architecture, and the way the CPU is programmed to carry out how it processes information, but unless you are a dedicated gamer or use a lot of high powered photo editing, or have the computer hooked up to a meter that measures in nano-seconds, you'll never notice the difference. There are certain instances where you might choose an AMD over an Intel or an Intel over an AMD, The Intel i7 has an onboard video controller, and memory controller and AMD doesn't, but if you're a dedicated gamer, you're not going to care about an on board video controller anyway because you're going to have a top of the line video card or two in your system. But it's the specialized things that you are going to be doing that will determine which companies CPU based computer you go with.
In your question you stated that you were not going to specialize in anything, i.e. gaming. You stated that the most advanced thing you were going to do is some photography, so as your new computer is just going to be a general use computer I'd suggest the most inexpensive computer that will do what you want to do with it. A lot of people will choose Intel over AMD because EVERYONE has heard of Intel, because they advertise all the time. Well, the advertising is not free, and the money for the advertising has to come from someplace, so next time you see an AMD, and Intel based computer side by side and the only difference is the price and the CPU, ask yourself if you want to spend the extra money for advertising, or if you want to pay for a night out with the money you saved.
Also whenever I've compared computers I've also noticed that the AMD based computer always came with more things in it, such as bigger hard drive, better video and things like that.