Which is better, a solid, hydraulic or roller lifter cam?

This all depends on what you're doing with the engine. There's no substitute for roller cams, period. The name of the game is flow. Heads don't flow if the valves aren't open. Roller cams have lightning fast ramp speeds. In other words the valves snap open and slam shut much faster than flat tappet cams, which means the valves are open wider for a longer period of time which makes for much more flow. More flow = more power.

A slower ramp speed cam, like a flat tappet type, opens the valves slowly where the steep / fast lobes of a roller cam (in retrospect) already have the valve wide open in the same amount of cam rotation, thus more flow into the cylinder. On that same note, the slower ramped flat tappet cam needs to start closing the valve sooner, and while it's closing, the roller cam is still holding its valve wide open and is still flowing fuel and air (or exhaust) until the very last second... and then SNAP!... it slams the valve shut.

The aggressive profile and ramp (lobe) speed of a roller cam also has its drawbacks. A higher lift and faster ramp speed needs stiffer valve springs otherwise you'll end up with valve float, which isn't good. Stiffer valve springs require screw-in studs or you'll rip the stock, pressed-in studs right out of the head. Stiffer springs also increase the load on the push rods, so heavy duty push rods are needed. High lift cams add more movement and friction to the rocker arms, so roller rockers are pretty much a must. Most billet steel roller cams require using an aluminum/bronze distributor gear which is very soft and doesn't last very long. Just like Newton's law; for every action, there is a reaction. Engines are the same way. Increase the load in one place and you'll surely increase the load (or friction) in other places.

Technology and metallurgy are changing. It use to be that a hydraulic cam wouldn't be very good for a hot street or a mild race engine when in fact, they perform very well. As long as good matching valve springs are used with a set of good quality, light weight lifters, there's no reason a hydraulic cam can't do well on the street, or on the track, and if someone tells you different, have them tell that to the guys running hydraulic cams at well over 7000 RPM in 11 and 12 second street cars.

Solid lifter cams can be a good choice for a hot street or race engine. They usually have faster ramps (lobes) than hydraulic cams, but not as fast as roller cams. They also need stouter springs than a hydraulic cam, but not nearly as stiff as a roller cam. They're kind of the middle of the road between the hydraulic flat tappet and roller cams.

Forget about those lame wives tales about solid lifters always going out of adjustment! That's just not true! We're not in the damn 60's and 70's anymore! The ONLY way the adjustment (lash) can change is if something is either wearing out or going bad, period. If a rocker stud starts pulling out, the lash will increase. If the tip of the valve is getting hammered or mushroomed, the lash will increase. That's what hardened lash caps were made for before we had better material to make valves out of. If the tip, or the cup, of the rocker arm starts to wear out, the lash will increase. If a push rod bends or wears out one (or both) of the tips, the lash will increase. If the lifter is getting cupped or the cam is going flat, the lash will increase. If a valve seat "sinks" or recesses, then the valve is actually lifting or sitting higher, which means the lash will decrease. No matter how you slice it, if a solid lifter cam keeps going out of adjustment, something is seriously wrong or isn't up to par! If nothing is wearing, bending, pulling, mushrooming, backing-off, or getting longer or shorter, then there is zero reason for the valve to go out of adjustment.  Guys that say solids will go out of adjustment when using modern components, such as stainless steel valves, screw-in studs, roller rockers with tool steel cups and rollers, hard valve seats, chrome moly push rods, etc, then it's just a wives tale being spread by people who have probably never even ran a solid lifter cam in a real engine before. If you're talking about an era engine with era components in it, well then you just might have to do some adjusting from time to time, but not when you have a modern performance engine, or a 1st generation engine with modernized components in it.