I prefer the Petrov because I don't like the doubled pawns in the Berlin Defense.
However, which one is more objectively solid? Which one is harder to crack?
If playing non-GMs, there is no need to worry about anyone cracking anything.
At class player level, I'd say neither and put my bets on the Caro-Kann. White has a lot of interesting attacking tries against the Petroff (my favourite being 5.Nc3!?) and it requires deep understanding to play the Berlin Wall with Black.
At GM level, I'll take the Berlin, for the simple reason that even Kasparov was unable to crack it.
The Berlin Wall is probably not good for anyone rated under 2500, and it may not even be good for anyone rated under 2650. When Vladimir Kramnik trotted it out against Kasparov in 2000, the shock was that Kasparov couldn't break it.
There are some excellent analyses of the Berlin Wall, but the brilliant idea behind the Berlin is simply that the endgames are incredibly difficult to play well.
The Petroff is an excellent opening for anyone up to 2500, and perhaps all the way up to 2900! The Russian Defense is not at all drawish except among chess professionals, and even then players such as Vishy Anand can play for the win as White.
So clearly, the Russian Defense should be preferred over the Berlin Defense for anyone not named Kramnik.
If I remember correctly, Kasparov hasn't faced Kramnik's Petroff. Maybe Kasparov might have difficulty with the Petroff as well.
According to chessgames.com, Kramnik has used the Petroff 102 times compared to 47 times with the Berlin Defense. Both the Petroff and Berlin Defense are called "drawing weapons". Since Kramnik prefer the Petroff more, does that mean the Petroff is more solid?
Kasparov cracked Kramnik's Berlin Defense:
Though the berlin defence does end in a draw often enough I would not call it a drawing weapon.
Right from the opening black creates inbalance (bishop pair vs pawn structure and kingside majority // position of the kings etc). These inbalances give black something to play for and if white makes a mistake capitalize upon. It is not for no reason that a player like Aronian says he plays the Berlin if he wants to win.
These inbalances are amplified at amateur level because we are weaker with the several advantages each side has. It is very easy to exchange the wrong pieces and end up lost and this goes for either side !