Apollo is a private equity firm, so they are most likely acquiring Rackspace because they see fat they can trim (read: laying people off, outsourcing labor, tax optimization) off a decently competitive company that they can possibly take public or sell in 5-10 years.

It's not so much about competing with Amazon, Google, etc. or advancing the state of the technology as much as making a bet that the brand is currently undervalued and that conditions in the cloud computing market will allow for a profitable exit in the medium term.

For examples of Apollo bets that have gone wrong see its LBO of Harrah's (basically bankrupt) or Linens 'n Things (bankrupt).