I have stayed at both PO-Riverside and the Caribbean Beach Resort and you can't go wrong with either one of them. However, because I prefer the caribbean theming over old south, I would have to say CBR is my fave of the the two. But I will break it down:
Theme: As I stated above, I prefer the beach theming of CBR over the old south theme of PO-RS. But that being said, they are both lovely resorts! I am just a big fan of CBR's white sand beaches, the lake and colorful buildings. PO-RS does not have a beach or a lake. The river at PO-RS has been dyed brown to look more like the Mississippi River I would assume. I love water, so I just prefer to lay in a hammock and watch the world go by at CBR!
Food Court: I prefer the one at PO-RS over CBR. Pizza and chicken tenders taste pretty much the same WDWorld Wide but the burgers, breakfast foods, dinners are better at PO-RS in my opinion. Plus you also have the option of eating at Boatrights, a sit-down restaurant that is open for breakfast and dinner and is wonderful! Yes, CBR has Captain's Tavern but their menu is limited and I believe they are open only for dinner. The food court at PO-RS also has a larger seating area where I usually feel a bit crowded in at CBR. Both food courts are noisy, but CBR's seems much noisier.
Transportation: In my experiences, CBR has the better transportation. Less wait for buses, more buses running during busy times etc... But things may have changed since PO-FQ closed and there is no longer one system shared between the two resort.
Pools: About equal IMHO, both are nicely themed. It seems the quiet pools at CBR are less crowded than the ones at PO-RS though and there are more of them too. As two adults with no children we prefer to use the quiet pools.
Rooms and Housekeeping: The rooms at CBR are a bit larger than PO-RS but truthfully your hardly notice the difference. Both have 2 double beds or 1 king bed, double sink vanity, a table with two chairs... If I understand correctly from SeaSprays recent report (thank you SeaSpray!!) that CBR has a coffee maker and a privacy curtain to divide the vanity area from the bedroom. Last time I stayed at PO, they did not have that feature. Housekeeping at both resorts has been excellent in my experience!
So either way, you can't go wrong. They are both excellent resorts. Enjoy your trip and please feel free to ask me any questions.