I haven't used the vortex reddot, but based on the quality of their long range optics, I wouldn't hesitate to give one a try.
I am currently using a vortex viper PST 4-16x50 EBR-1 MOA on a 308, and a matching scope in 6-24x50 on a 338 lapua mag, and they will run toe to toe with the leupold mark 4 ER/t. I have shot a Barret m82a1 with a vortex razor hd, and ot was comparable to the Schmidt & bender the marine corp is mounting on their m40a5.
If someone told me that vortex's reddot will hold it's own against an eotech or Aimpoint, I would believe it until I could prove it wrong.
What budget are you looking at because there are some models of eotech that can be had cheap, like $300, and it is IMO, the best sight platform for a short range AR setup.