For some purposes, studio light can be better than sunlight, for some definition of better. Specifically, it is more flexible and easier to control.
Light has a number of fundamental characteristics, including intensity, direction, and spectrum. You can find more on these under What's the technical difference between artificial and natural light?.
The sun is very powerful, which makes it better for lighting entire landscapes than studio lighting. On the other hand, it's hard to move around; if you want light coming from a different direction, unless you are a mad scientist or have the Biblical powers from Joshua 10:13, you have to wait for the earth to spin into the proper place — while hoping the weather cooperates.
That last is another factor: sunlight is generally found outdoors, where weather is a frequent occurance. You can get the sunlight indoors using windows or skylights, but since these are generally fixed in walls and ceilings, they limit your flexibility even further. And while equipping these with glass technology will help in the event of rain, the sun will still be covered by storm clouds in that case, making it not much use.
Additionally, because the sun is very far away,, the relative falloff of light will be smaller than that from a very close light source. That is, the effect of a small light right out of frame will be different from that of the sun even if the small light is the same relative size from the subject's point of view. (See Is there a difference between a large, far light source, and a small, close one?). Again, moving the sun closer is very difficult, and also likely to end all life on earth, so studio lighting is a big win there.
And, it's not just direction: the portable nature makes it much easier to attach and manipulate lighting modifiers. You can (and people do!) put diffusion material over windows, or use reflectors, diffusers, flags, and more in sunlight — there's an infinite realm of possibility there alone. But you're still constrained by the basic facts of nature; with artificial lighting, you work with different constraints (a bigger infinity, if you want to think of it that way).
The spectrum and light color is another issue: because the sun is a miasma of incandescent plasma, it's quite ideal for the accurate perception and rendering of all colors in an object, scene, or person. See What is Colour Rendering Index (CRI)? for a lot more on this. And also see a number of questions and answers about color temperature — What is color temperature and how does it affect my photography? is the basic one, but I also like How to recognize different lighting color temperatures?. In short, the sun is way better for color than low-cost fluorescent LED lighting, and moderately better than higher-cost versions of the same, but for most practical purposes this isn't an issue when using studio strobes, hotshoe flashes, or "hot lights" — incandescent of any sort.
In short, control is the thing, both because it increases versatility and because you can do the same thing over and over again without waiting for the time and weather to come around again.
For your specific case of digitizing family photographs, I really think it's easier to get good results with a moderate-cost scanner than with an elaborate setup with a DSLR — even a nice DSLR and a very elaborate setup. But if you do go with that, you probably want artificial light, because it'll be much easier to get consistent results.