There is no "ballpark percentage". Someone DFW based would have a much different ballpark percentage than someone based in MCO, for instance. I'm DFW based and I'd guess I average complimentary upgrades probably around 40-50% of the time but it's insanely hit or miss. One time I was 4th on the list from LAX-DFW on a systemwide (Connecting DFW-EZE on a confirmed SWU) and didn't clear the LAX-DFW leg. Other times I've been lucky to snag some some great complimentary upgrades such as DFW-HNL and KOA-DFW. I'm almost always successful T-100 confirming an upgrade from JFK-SFO but good luck clearing DFW-SFO. So it's just hit or miss especially if you're hub captive to DFW like I am.
Your companion should upgrade right below you on the list so if you're 1 and 2, and there are two seats, you'll be fine. Sometimes problems happen when the traveling companion has his or her own status and then the upgrade priority splits- however the Admirals club/ checkin should be able to fix that.
The only thing different with award tickets vs. paid ones is that you're below all EXP who are flying on a paid ticket. Other than that, no difference.