What I'm concerned about is their performance running Windows 10. I've heard that some computers with windows 10 make a lot more noise than usual (or at least their fans do). I'm worried that if I buy the Lenovo it will make a lot more noise running Windows 10 because of its weaker processor.
Not sure where you read the above but it is a bit off in suggesting that computers running Windows 10 make any more noise than if running any other OS.
What can make a difference is if the graphics are provided by the CPU as opposed to an add on video card or a graphics chip that is integrated into the MB, this is because the CPU has to work harder and depending on the type of load that the computer is under the CPU cooling fan may run faster and for longer at higher rpms to keep the processor cool.
Budget asides for now, your purchase should be based on what the main use of the computer will be, if only for school or office type work then an i3 CPU with integrated graphics would be fine but when you bring gaming or streaming videos into the equation you are better off with a computer that has an add on video card and better case cooling as standard, something that you do not always get with brand name pre-built computers.
Let us know what the main use of the computer will be and post links to the two computers mentioned in your OP and we will take a look at them for you.