Both are excellent openings. Solid is in the eye of the beholder. Both openings can be learned at a rudimentary level in a weekend and both will serve you for the rest of your life.
Against top players, the QGD tends to be a bit more passive than the Slav. So if you want to strive to win as Black, the Slav is probably a slightly better choice.
For novices (and for people asking the question), The QGD Tarrasch is probably the best way to get a good playable position. That line goes:
1.d4 d5 2.c4 e6 3.Nc3 c5. The center usually opens up and Black gets to develop his minor pieces comfortably. The only drawback, and it's a minor one, is that Black usually has an isolated queen pawn (IQP). But even that is good because as Nimzovich stated, learning how to play with (and against) an IQP is a major step toward understanding positional chess.
Which one is harder for white to beat? Which one is more solid?