Right now, cheaper by 50x-100x. My node typically has fees about 1.5% of what Visa would charge, and even less for smaller transactions. Once blockspace becomes consistently scarce however, fees could rise closer to Visa levels.
Discussion
Correct, for the OP I was thinking more about future high fee scenarios...
It’ll be interesting if there will be a difference between fees on new channels and fees on old channels. I believe routing attempts to find the lowest fee paths, which could mean there continues to be downward pressure on fee amounts as high fee nodes receive less transaction volume.
Definitely agree that it will be higher than it is now, since it’s still essentially free.