I much rather have lock-picking strictly character based. No mini-game at all. At the very least, they should have made it the same as FO3. If you did not have the appropriate skill, you could not even attempt to pick the some locks.
I am very glad they did
not carry over that particular mechanic, because it only really works if you know in advance at what level of skill a character will be attempting a given lock.
One of the more egregious cases of this in FO3 was an ammo can in a Raider base on the opposite bank of the Potomac; most characters reached this base at a low level, thus low skill, but it had a difficulty of Very Hard so required 100 skill just to attempt it. Naturally, there was never very much ammo in it, which begged the question of why it was a VH lock to begin with.
FO1 and 2, on the other hand, allowed you to try any lock at any skill, but the harder the lock the more likely you were to fail, and low skill increased the chance of that happening. Failing carried real risk with it too, since there was a chance that doing so would permanently jam the lock; this meant that you couldn't just spam-attempt a really hard lock at low skill and expect to crack it, unless you got insanely lucky while doing so.
Skyrim uses the first half of that equation but leaves off the second, which makes picking locks a total joke; failure effectively has no cost since picks are limitless and the lock can't jam, so you have nothing to lose by spamming the lock until it opens.