Interesting question. I had thought batteries were still orders of magnitude more expensive than nuclear, but just looked up some numbers to try and get an idea. Caveat, these are just numbers I've looked up; they look reasonable to me, but I'm no expert, so could well be making a mistake here. Also I'm just looking at capital costs, not operation.
From what I can find, the capital cost of a new nuclear plant is somewhere on the order of $6M-9M/MW.
On the other hand, a 3MWh grid battery from Tesla runs about $1M. So ignoring cloudy days and just considering providing power overnight (in the winter), you'd need about 14 hours of capacity, so about $14M to provide 3MW, or roughly $5M/MW.
So, in terms of initial capital cost, just the battery portion to handle the overnight gap in solar production would be roughly equivalent to the cost of nuclear, but of course that doesn't account for the cost of the solar panels, nor for the fact that there will be other periods when generation is low. (Although these can be partially dealt with by over-building the renewable generation and using wind as well as solar.) However, the other issue is that the lifespan of grid-connected lithium ion batteries appears to be about 5-15 years, whereas nuclear plants should generally last several decades at least.
So, batteries + renewables are more expensive in terms of capital than nuclear plants, which are themselves quite expensive, but I must admit I'm surprised that the difference isn't even greater. I expect part of the problem is production capacity. You can build a 1100MW nuclear plant, but I expect it would be nearly impossible to buy a 14GWh of grid batteries because the capacity to build them in that scale just doesn't exist, yet at least. Also, as others have mentioned, you'd need a lot of space.
There are other methods of storage that are used, pumped hydro being the most common in large scale, but requiring specific geography. There are other options like gravitational storage with shafts and weights or carts on tracks or what have you, but they're all expensive and/or difficult to scale.