White LEDs are just a blue LED, with typically a single phosphor that converts some of the blue to other colors. All their spectral distributions look similar to this:
There is a single sharp peak for blue, since that's the true LED color shining through, but the phosphor emission is smooth. So there's little color enhancement, especially for reds, which are particularly weak. You can move to a lower K rating and get more red, but then you get more yellow too, and that doesn't make anything look good.
On the other hand, T5's can use multiple phosphors, and be engineered for any number of color-enhancing peaks, like the infamous DD Giesemann Midday:
This is one of the major reasons I built a dimmable T5HO fixture for my largest and showiest tank, instead of LEDs. I really wanted to bring out the colors, and I don't think LEDs can do that without some trial and error, which would be expensive on a fixture this size. Eventually I'll play with LEDs on smaller tanks. I expect to come really close to a good T5, it'll take some red LEDs mixed in with the white, maybe some other colors too, and possibly some diffusion to avoid multicolored shadows.