Solar:
https://en.wikipedia.org/wiki/Topaz_Solar_Farm
The Topaz Solar Farm in the US has a capacity of 550MW and a construction cost of $2.5b US billion.
That puts it at a cost of $4.5 million per MW capacity (550MW / 2.5b) (adjusted for inflation that's $3.2b USD or $5.8m per MW). It is used at 26% of its capacity which I assume is due to the non dispatchable nature of solar (would likely change if batteries were added - increasing cost).
Assuming a 10 year loan at 3% adds $500m bringing it to $6.7m per MW capacity
Nuclear:
https://en.wikipedia.org/wiki/Palo_Verde_Nuclear_Generating_...
The Palo Verde nuclear plant has a capacity of 3937MW and a construction cost of $12.6b USD adjusted for inflation. That puts it at a cost of $3.2m per MW capacity and it was used at 82% of its capacity over its lifetime.
Interest at 3% over 10 years adds 2b to the figure making it $3.7m per MW capacity
Limitations:
This doesn't consider running costs, maintenance or factor how usage capacity affects cost.
Maybe I am missing something, perhaps the running costs of nuclear eclipse the total cost of solar + batteries over 50 years? Maybe the loans granted for nuclear are at a much higher interest rate than those granted for other power projects? Is insurance a factor?