Your requirements are very mixed: you're intending to use the machine for a wide variety of loads, with the software suite likely to be fairly dynamic (almost always the case for systems used for development).
It is unlikely that you will notice any meaningful difference due to your choice of processor implementation for such a mixed workload, and if you want to optimise for some specific workload, it is much more likely that a particular chip series would be best for that, rather than a specific manufacturer (as both vendors you list have a wide variety of chips, and while one may currently have a chip that is better than the other for some workload, it is exceedingly likely that the number two chip for that workload is from the other vendor, rather than a chip in a different product line from the first vendor).
Servers are frequently most limited by I/O bandwidth, unless your described development activity includes significant computation. As such, hardware that provides more or broader I/O channels tends to perform better for many of these workloads. Review system diagrams, and look for an architecture that has the fewest potential bottlenecks for exchange of data. You may also want to get significantly more RAM than you think you need, to serve as disk cache, and reduce load latency for frequently-accessed data.
Nettop or similarly extremely small form-factor devices as you've referenced are typically optimised for low power usage, which tends to mean that they have reduced I/O bandwidth, or bandwidth optimised for streaming a single source of data, and may feel more sluggish as a server than they might say, as a media player. On the positive side, the low power optimisation tends to reduce or eliminate concerns about cooling.
I've comfortably run Ubuntu Server, providing mail and web access along with other workloads with as little as 512MB RAM, and with processors as slow as 700MHz. Unless you looking at extremely small devices (plugservers, etc.), it is unlikely you will find anything in retail channels that cannot comfortably run these services. That said, depending on the load (lots of mail, lots of page views, lots of computation, etc.), you may find that you need more memory, processor speed, I/O channels, etc. Any developer using the server will never be satisfied with the performance, because they will find something that takes a while to run (I've heard complaints from folk with 128 cores and 1TB of RAM, with broad-multipath IO to secondary storage).