There's no general rule, and your question will be closed by a moderator soon as being too general.
In general the trend I've seen is start on AWS, and once you hit Dropbox scale you can save a fair bit of money if you create your own infrastructure. That takes a lot of planning, work, and more people of course. Netflix however are all-in with AWS.
Have a look at the AWS calculator and work out what your monthly costs would be. Assume your developers won't turn off the test / dev VMs, and make sure you look at reserved instances (note - they can be sold if required). Compare that with the hardware costs you expect in the next say three years, including administration. Of course you still need to administer AWS systems, it's just that the skills are different, and in some cases the ability to automate is provided.
AWS also has a total cost of ownership calculator. Keep in mind it's advertising for AWS, it's not necessarily meant to be objective and fair, and assumes you need to buy all your hardware new.