Hearing protection is rated by db reduction and all hearing protection has a rating label on it that is specified by the government. I doubt noise cancelling headphones are considered hearing protection, but if they are, they will specifically be labeled as such.
As someone who has worn hearing protection of all types, on firing ranges, industrial circumstances, and while cutting the lawn, here is my $0.02: Any hearing protection is better than none. Cheap, disposable, foam plugs are as effective, or more so, than the muff types depending on the db rating as long as they are inserted properly. Adults should be able to insert plugs properly but kids probably can't. Muffs work great and are good for frequent on and off situations, plugs take more time and effort to put in. Muffs are hot and sweaty when it is hot out. Expensive electronic muffs work well from a safety standpoint, but I find the electronics worthless, especially on a firing range. They amplify every small sound like people loading magazines etc and make them all equal. So, the range commands and somebody zipping a bag shut are all equal and therefore impossible for me to discern. I've used several electronic muffs and I think they are all equally worthless, other people swear by them.
So, for mowing the lawn, cheap foam plugs work great and don't act like two little ovens around your ears. On the firing range, I wear both, plugs and muffs. I don't care about the heat and sweat from the muffs because I want the extra protection. Also, I can pop off the muffs to have a conversation and still have the plugs in. If you wear both, you add 10db to the higher rating of the two devices. So, 30db muffs+ 30db plugs = 40db total reduction. Plugs are nice because you can stash them various places, like your glove compartment etc. I work in and industrial setting, so I just grab a handful here and there when my stash runs low.
Any $15.00 set of muffs from walmart or Academy are fine. Just get ones that fit comfortably and they should all be rated around 30db or so.