Since the other people here cannot seem to give a comprehensive answer I will.
Intel is known for having better processors overall and are more openly supported while been a normally higher quality product then those that AMD produces.
Intel is more expensive per dollar but having better performing chips, they don't run as hot as AMD does and they are very power efficient.
AMD on the other hand is cheaper and they run like a volcano and drink more power and produce more heat then the Blue Dwarf star, but on saying that you get a lot more bang for your buck and if you get the black edition they will overclock like no ones business.
So it really comes down to personal preference and what you intend to do with them and also your level of skill AMD is more orientated towards the computer literate and overclockers that know full well they run hot and require liquid cooling if pushed too hard, they are also cheaper and therefore slightly more poorly made.
Intel on the other hand is more beginner friendly as their processors will control and variate temperatures by default with thermal throttling unless told otherwise and if you don't intend to build an enormous beast machine with everything pushed as high as possible they are a very good option and will not disappoint.
But if you are looking for a budget CPU for nothing more demanding then gaming trust me you will not even need a Sandybridge i7 so the best budget CPU for you would be either an i5-4690T which retails at around 213 USD or 145 quid or if you are intent on an i7 I would recommend the i7-4790 which retails for around 220 quid I think as these will both be more then enough for gaming.
And on the AMD side I would recommend the FX-8370E black edition.
Hope this helped and if so leaving a like or reply is appreciated.
Intel for everything, Amd for almost everything..
AMD is the superior brand when video editing and using allot of cores since it has 8.
Intel is great for gaming and also, video editing but processors like the AMD 8350 will dominate the 4770k in video editing whereas the 4770k will dominate it in gaming.
If you don't have the money go amd. (you can over-clock these a lot usually)
If you do have the money go intel.(quite good not much else to say)
My only dislike towards intel right now is they change the socket too fast(probably to make more money)