Hi, Heather! How great you are traveling across the country to visit Disney World! Glad to have you!
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Beach Club is an amazing resort. It is in the Deluxe Category, so you will have a larger room than you will at Port Orleans Riverside. The best feature at Beach Club is the pool, Stormalong Bay. It is something your kids will love! This resort is within walking distance to Epcot and just a short boat ride away from Hollywood Studios which I know is of interest to you.
Port Orleans Riverside is a Moderate Resort, but very nice! The grounds are beautiful to walk around, and it is quite peaceful.The large food court is also nice with kids. From this resort, you can take a boat shuttle to Downtown Disney which is a nice feature.
With staying 10 nights, you might enjoy the fancier pool and extra space you get at Beach Club. Also, it truly is nice walking to Epcot in about 10 - 15 minutes. If your vacation budget allows Beach Club, it is a nice choice, but if you find POR is more along the lines of what you want to spend, I think you will like this resort, too!
Although you live near Disneyland, give Magic Kingdom a try! It does have some rides that overlap, but I think the 2 parks have such a different feel to them! The same goes for Downtown Disney. I think you will enjoy seeing some similarities, but it is fun seeing how different they are as well!