Our house is 104 years old, there are several styles of windows, including casement and double hung (newer) windows.

Esp. since they'll be on an addition, I don't see why they can't be different, as long as they share something in common.

Our double-hung windows have grids that mimic the lites in my casements. But I also have windows that have three vertical sections, and some that are just plain double-hungs. Viva la difference!

Another old house owner here with eclectic windows. This 1890's house was modified several times and they used a couple different window styles, but overall they work together. I don't see that it would be a big problem for you unless the windows were clearly very incompatible with what you already have.

Personally, in a sunroom I would do large casement windows and not double hung type. That doesn't answer your question though :).

We converted a screened porch into a sunroom. It's quite obvious that this is an addition and not an original part of the house (which is fine). The 8 dbl hung windows we put in don't match those of the rest of the house. I think it would look more weird if the windows matched since the built part doesn't!

Are the windows in the rest of the house going to be replaced sooner rather than later? Is there a chance that at some point down the road you'll change out the rest of the windows to dbl hung?

Either way... you do whatever you want and have whichever you think you would like.

Jane, I think it depends on the house and the window placement. I don't see a problem with casements and double hungs in general. Some factors unify different kinds of window, like divided lites or grids, or using similar proportions throughout. For example, having a horizontal spread in one area and a more vertical orientation somewhere else might look hodgepodge. Sunrooms might qualify for a stylistic exemption, tho, since they're a special kind of room!

If you have a picture of the outside that shows the sunroom and the main part, that would help.