You appear to have a lead closet riser, so you can't take that existing toilet flange off without creating a bigger problem...so, a repair ring with a good seal beneath it is your best bet.
The concrete was probably installed around the flange, so if you did need to replace it, you'd have to crack away the concrete and probably replace the lead as well. A CI toilet flange is typically leaded in place as well, but may not be with a lead riser.
Because they did not tile up to the flange, that might restrict the toilets you can use to cover that hole as well. While it takes a little more skill, when tiling a bathroom, it's best to run the tile up to, and actually under the toilet flange.
Keep in mind that the toilet bolts are best thought of as aligning the toilet, not really holding it tightly in place. Once it is snugged down, adding some caulking around the base of the toilet (leave a gap behind unless your locale prohibits that) will keep it from moving, allowing the wax ring to keep the seal intact. Movement will damage the wax seal. Excessive tightening of the anchor bolts will potentially damage the flange, but could also just as easily break the base of the toilet. Those bolts should just be snugged up once you've compressed the wax with your weight on top.