I'm not going to get involved in the various merits of the Peak products v DE-5000, I have seen mixed reviews / reports on them both. That said however I can take sides partially here with bd139 in as much as PEAK gear is British made and by all accounts their service back is, so I'm told first class.
I have neither of these devices so I'm not qualified to comment further on them.
I do however have (IMHO) the excellent XJW01 and also a Chinese component sorter tester of the sort that Dave tested
https://www.youtube.com/watch?v=7Br3L1B80ow, and I can say with complete honesty that both are very good at giving me a reasonable reading for ESR on caps.
The M-Tester does give me a quick and dirty means of identifying if a suspect cap is either short circuited (yes a DMM will do the same) or if it has a totally stupidly high ESR reading which will cause circuits to fail. If I want to know what the ESR is at a certain frequency then the XJW01 allows me to select a frequency (not RF through) and they both agree pretty well. The XJW01 is a 4 wire device so is best used for caps etc that have been removed from the circuit.
Once the equipment being worked on has been brought back to life, then if the device is going to be useful and part of your normal test items, then I'd agree that the best approach is to replace all the caps with new ones to avoid it breaking down when you most need it. That is where the simple ESR meters really come into their own, as bd139 rightly said, it is not essential to be mega accurate, all you really need is a ballpark figure, a sort of good/bad indicator to get the equipment working first and foremost. To just go ahead and replace all the caps without getting it working first, could be just a wast of money and time.