Solids
The biggest problems with solids is that they are neither throttleable, nor can they be shut off (at least the existing design). The grain can be modified to alter thrust during burn, and there have been tests of blow-out ports to kill thrust for shutoff, but a liquid gives you a lot more flexibility. Not to mention higher performance. You could stick a simple "big dumb booster" stage in there and do just fine.
Griffin likes this design, and the solid booster makers, seeing the end of the Shuttle coming down the pike, are pushing it hard.