I am having the exact same problem. Photoshop, when reducing image size, remained crisp, regardless of the resampling, which I never had to check. If I uncheck the resample option, Affinity makes no change to the image size. If I leave it checked, things pixelate. This is going from high-res to 72 dpi...standard for web. I've tried various options. The following image is from a high res (2362px x 2126px) image...down to 300 px wide (and, small note, when I leave the lock on width locked to height, I don't see the height recalculate...it's a minor issue if the resizing actually worked well). The attached is with Bilinear resampling, but the results were similar with all others, if not worse... *(the below preview is not 300 px wide...but when viewed at 300 - particularly on the purple text, the pixelation is terrible). I am working with designers who cannot have this, and I just shelled out $80 bucks thinking I could move away from Photoshop.
My apolgies - it is displaying at 300px wide...but I need it larger than that, and the large I make it, the more pixelated it becomes (not enlarging this image...just reducing the original to say 600). But event the one above is not as clear as it should be.