Solid-tipped rods are great for when you're either twitching a very light lure, straight-retrieving a light lure, or fishing down the side of a wall.
The subject of solid-tipped rods today is actually far more complex than it used to be. Just as tubular tips vary in action and taper, solid tips do too - but even more so. Solid tips can be long or short, with a fast or slow taper. For example, a short, very fast taper solid tip may feel quite stiff in comparison to a very long, slower taper tip and be great for twitching a lure aggressively. However that longer, slower tip may be better for straight-retrieving or fishing down the wall when you want the tip to provide less resistance when a fish takes. It may feel quite soft in this style, but can fish incredibly well in the right situation - catching you more fish than another tip style - solid or tubular.
The only thing that solid-tipped rods typically share with eachother is that the solid tip will be softer than the rest of the rod that it's attached to - but that's not saying much! This will always ensure a fast action. But some are still faster than others...
My own pick just recently was a Tailwalk Ajist SSD 710. I love this range for the fact that they sit nicely in the middle with regards action and feeling. With a solid tip that's not to stiff or too soft, they make superb all-rounders. I like longer rods so have gone for the 7'10", but appreciate that a lot of anglers will find favour with the shorter models. Just brilliant, easy to use, fun rods no matter which model you go for.