Interesting point CFO, if you want to look at the price vs performance then the passive headsets will win, as they offer a lot of noise reduction at a low price point. As these have been steadily developed to the point where we are now, you can get a good passive headset at a very reasonable price and fly for ages using them. The thing to realise here is that these headsets won't develop much beyond where they were 20 or 30 years ago. The only way forward from there was to add active noise reduction, but unfortunately it comes at a price. Bose first introduced it in the 90s, and fortunately prices have dropped since then, but they will never get as low as for a passive headset.
ANR has now matured to a point where we can use it to reduce the noise in an otherwise not-so-good passive headset, such as the Bose A20. As this headset was never designed to be used without ANR, you will notice it when the batteries go dead. Same thing goes for some of the in-ear options with ANR, although those have their own pros and cons. 20 years ago the only good in-ear headsets (as far as I can tell, but I never looked into this much so I might be wrong) were based on moulded inserts, but another development has provided us with loads of different in-ear tips in different materials that provide noise attenuation on a par with passive headsets, or better. So we can now develop headsets that don't need to rely on passive noise attenuation first, providing more or different levels of wearing comfort, and use the ANR to sort out the major part of the noise issue. If you don't want to rely on the batteries alone (it will become second nature to carry spares after a while and lithium ion rechargables last a long time), look for an ANR headset that's based on a good passive one, such as the DC H10-13X. Going down the ANR route will incur a cost, but the way I look at it I will recoup that at the end of the line by being able to avoid hearing aids for a little while longer.
Headsets are very personal, for example some people can't stand wearing in-ears very long, or can't find the ideal in-ear tip to fit their ear canal anatomy. Others can't stand the pressure that an over-ear headset exerts on their heads or the weight of a particular model, or the interference between the headset and their (sun)glasses. Also, each and everyone's perception of sound is different, so while I can easily tell the difference between my first, cheaper and earlier generation, ANR headset and my current one, there will certainly be pilots who won't mind the difference between a non-ANR headset and a top-of-the-line Bose A20. In a video from one of the US pilot shops several headsets were reviewed (See below) and they didn't just comment on the difference in noise coming in, but also on the clarity of the radio and intercom, and one I hadn't considered: the quality of the microphone. It's not something you'll notice much yourself, but there are some significant differences in microphones and it does help sometimes to be more easily understood by others. It also made me think of another pro-ANR aspect: you'll be better equipped to deal with other crewmembers' not-so-good microphones!
Right, that's my two cents, all boiling down to: try as many of them as you can and go for the one that suits you.