Only ever spec'd N3K to connect servers. The 3172 is a great value DC switch provided you don't want FEXs or ACI. Personally, I wouldn't be brave enough to spec one for campus distribution. I think the N56K is better suited to this role but more expensive. As Reza states, Cisco has in recent years pitched their NEXUS switches at the DC, although in recent months they've been shifting towards a more open minded 'whatever suits best' approach.
The 3850 is well suited to the job but can't be split across comms rooms if that's a requirement. They don't have great egress buffer capacity either. I think the new 1G/10G model has 6MB per 12-port ASIC.
I'd opt for 4500-X myself. It's designed to cater for the distribution layer and has pretty good egress buffering (32MB shared) to cope with 10-to-1G contention that is commonplace within the distribution layer.
If you want a really great distribution switch then the new 6840-X Series is excellent and makes available 3000+ features, but they cost quite a lot more.
4500-X VSS will negate the need for a FHRP within the distribution layer.
As Reza stated, ensure your required features are all included in the N3K and don't trust Feature Navigator. Data sheets can also include false information. Software release notes are the most reliable source in my experience.
Not sure what distribution features the N3K would likely be missing. Full Netflow and Medianet features such as Performance Monitor are likely to be unsupported. The 4500-X can also perform network validation tests by generating synthetic video traffic based on pre-defined video profiles such as IPTV and IPVSC.
Perhaps not relevant to you but Prime Infrastructure offers much less support for NEXUS switches.
Incidentally, which 4500-X model did you price compare the N3K against? Perhaps the 16-port will be sufficient if you're stacking your 2960-X Series.
