Should be similar performance. But the 580 will consume more power. Depending on the pricing you are looking at though, for not much more, you might be able to get the gtx 1660 or 1660 super. I just got one of those for 230 US. From what I've seen the performance on that card should be closer to the 1660ti.
If you do go that route, I wouldn't bother with the standard 1660. The super would be close to a gtx 1070 level of performance.
Of the 2 cards you listed, the 580 may be slightly better. But can use over 200 watts of power under load.