IEMs with good earpieces are probably a better bet – the triple flange or the foam comply types are very effective.
Active noise cancelling are only any good on constant noise, so transients like babies crying, etc, aren’t handled so well.
An ear blocking IEM will be good with everything, plus the sound quality is going to be better.
For the cost of the big over the ear Bose’s you could get some Shure 535s which are seriously good headphones.
Plus the IEMs are wearable if you are trying to sleep and have your ear on a pillow.
I note that Bose now do some noise cancelling IEMs which might be worth a look. They get good reviews on their site but that doesn’t mean much as one says
“Once again Bose gets it right.”
whereas in reality Bose rarely get it right…