What is the difference between reliance on miners on Drivechains and Lightning? It's commonly said that the Drivechains proposal gives much power to miners and that they can steal money from these drivechains, but I keep thinking that if what they can do is to vote on which transaction will be able to spend from the hashrate-controlled escrow, then if a majority of miners collude they vote on a steal transaction, fine.

Now, a majority of miners can also steal the funds from Lightning channels they're participating in if they are able to spend an old channel state and don't allow the new state or the penalty transaction to be published in time.

Some differences between the two steal attempts are:


To steal on Drivechain the colluding miners don't ever have to orphan blocks.
They can steal all the Drivechain funds at once.


Are these the crucial differences? Do they make Lightning inherently safer than Drivechains? What am I missing?
I would consider these two crucial differences, so I guess you answered your own question. I guess the more important distinctions, though, are about the systemic impact of both:

Firstly, Lightning can simply be done with bitcoin as it is (OK, we needed segwit, but we needed that anyway). So it would be hard to keep people from using Lightning. 

Secondly, the risk of miners stealing bitcoins in LN channels is probably not a problem: LN deals with small amounts, miners would have to collude with one side of every channel they want to steal, and breaking Bitcoin's censorship resistance in order to steal some LN funds would be such a nuclear attack that it would probably tank price AND lead to a PoW change. 

On the other hand, IIRC drivechains explicitly expect miner consortiums to steal funds in unpopular sidechains. Very different risk profiles IMHO.