For tl;dr, definitely take the FullHD one.
In slightly longer, it also depends on the physical size of the screen. If it's the size of a playing card, 1280x800 will do. If it is larger than a phone I'd say you will certainly notice the difference between the two; if your picture frame is the size of an iPad mini or above, you absolutely will notice the difference.
If the price difference is huge, that's obviously a tradeoff, but if the price difference isn't too big a kick in the wallet it's worth the higher quality.
(For what this is worth, phone photos have greatly exceeded that resolution for a long, long time. Modern iPhones shoot quite amazing photos; can certainly see why you want to showcase them. ๐)