So, comparing the report in your link for cost, Solar PV capital cost is a bit more expensive than "Advanced Nuclear" capital cost. However, the ongoing maintenance costs for solar PV are less than 50% of the ongoing maintenance costs for Advanced Nuclear. In fact, the additional (over Solar PV), annual maintenance costs for Advanced Nuclear are about 17% of the entire capital costs. After just a few years, Solar PV will be saving massive amounts of cost over Advanced Nuclear, just in maintenance.
This seems to at least be partially taken into account in the "Total LCOE" numbers (sorry, but this report doesn't seem to have much as far as exactly how these numbers are calculated). Without subsidies, Solar PV is about 30% higher. However, when you look more closely at the actual ranges behind the averages that are the primarily cited data, you'll find that the Total LCOE estimate ranges for Advanced Nuclear and Solar PV actually overlap. The "minimum" Solar PV estimate is 97.8 and the Advanced Nuclear "maximum" is 101.0.
The claim that atomic energy has major advantages over solar is not borne out in this EIA report. In fact, the report seems to show that solar is highly competitive with almost every generation source and actually has a huge advantage in ongoing maintenance costs, being practically at the bottom.
I haven't investigated the other links yet, since the first one didn't seem to pan out.