* Also very late, but the thread was bumped, so, just in case... *
People on this site are great for finding the best value, and less expensive options for folks.
I only start with that because my recommendations are neither, but I use them both for mowing. And both were top ranked and as such more expensive. But they are both also last year models so bargain shopping applies..!
For ear buds I use Jabra Elite 75t Actives. These drown out almost all noise from the mower, and if listening at any decent volume, you won't notice the rumble around you. They also just came out with a Firmware upgrade for ANC that I haven't fully tested, (I'm in MI and my mower is in winter mode now) but I expect it will work even better.
For over ear, it's hard to beat my Sony Wh-1000XM3s. With the ANC on I truly heard nothing but music, even at lower volumes.
I'd recommend either option depending on your style preference and cost. I think the Jabra buds are down to about $150-$169 maybe, and the Sony over ear, were just on sale recently and should be again for under $200 also.