I'll assume that neither of you are nitrox certified, as this is the basic content of that course... but it is certainly a good question!
There is no hard evidence that nitrox really makes a difference in how one feels after diving, although many people swear that this is true. Of course, to really be sure, you would need to do a double blinded study with people being evaluated post-dive by some reproducible test of "well being", which has not been done as far as I know.
In a nutshell, the main advantage of nitrox is that it increases your non-decompression limits, that is, the amount of time you can stay at a given depth before acquiring a decompression obligation. This is because it contains less nitrogen per unit volume of gas, so tissue nitrogen loading is less (all other things being a constant). Furthermore, offgassing is more rapid the less nitrogen that there is in your breathing gas, this is why divers with a decompression obligation will often breathe from richer mixes (up to 100% O2) to reduce the time that you need to safely decompress.
Now here is the downside of nitrogen - oxygen is toxic above a certain "concentration" (partial pressure), so for every mix, there is a maximum operating depth (MOD). If you go below this, the partial pressure of oxygen will rise above a certain point (let's use 1.4 atmospheres to simplify things), putting a diver at risk of seizures. The abovementioned 100% O2 can't be used below about 20 feet for this reason. Also, there is a cumulative toxicity of oxygen that can cause other problems, but I'll leave that out for now to make the answer to your question a bit simpler.
So to settle the discussion between you and your fiance
there isn't much point in using nitrox at very shallow depths since you wouldn't see much of an extension of your NDL - in fact, I believe that the NDL on air at shallow enough depths is essentially infinite (that is, you are offgassing as fast as your are ongassing). As a practical matter, you would run out of air from a single tank even at slightly deeper depths before you would run up against your NDL.
Nitrox is most useful at depths closer to the MOD, where nitrogen loading is more of an issue, and especially as you get better at gas consumption so that you are more likely to be NDL limited as opposed to gas limited. For the common mix of EAN 32%, the MOD is around 110 feet, and for EAN 36%, it is about 90 feet.