Running some models myself using 4nec2...
The 0 model is horizontal, the other numbers are that many degrees below horizontal.
These models are mounted 18 feet above the earth. I also tuned all of them to resonance and did it in such a way that the vertical elements were the exact same length as the radial elements in the individual models.
Essentially, when it comes to gain, horizontal radials provides the most low angle (in this case 15 degree radiation angle) gain, and as you angle the radials down, that gain drops. However, you won't notice a difference in gain as the worst angle has -0.29 dB less gain from the model with horizontal radials. The more I angled the radials down the less gain the model had.
It should be noted that the exact opposite is happening with the higher angle lobe (up at the 45 degree radiation angle). As you angle the radials down, this lobe gets stronger.
When it comes to radiation efficiency, angling the radials down also drops the antenna's overall radiation efficiency. The difference between the horizontal radials model and the model with the radials angled down from horizontal to 60 degrees down is about 6%. Again, not enough in and of itself to be noticed.
One other thing to look at is the impedance matching results. In this case, R and SWR at resonance.
Horizontal radials show an R of 22.9, and an SWR of 2.18
Angling the radials down causes R to go up, and SWR drops to its low point at about 45 degrees. Angle the radials further than that and SWR starts going up again.
If you are someone who cares about SWR, the only real benefit to angling radials down is the lower SWR you can get. If, however, you are one of us that don't really care about SWR, as long as it is "close enough", then just adding a slight angle will be enough.
I want to point out that this is for a 1/4 wavelength vertical antenna, if you are talking about radials on a 5/8 wavelength antenna, downward angled radials can actually work against the antenna. If you want to see angled radials put on a 5/8 wavelength antenna model, ask and I will make some models for you.
The DB