Like A Time of War, MechWarrior Destiny is mainly based on human-scale interactions and combat. These can be converted for use in Classic, albeit with a bit more work in converting some things.
Where A Time of War is better for detailed, grounded campaigns featuring characters who often suffer very limited lifespans, Destiny is a narrative-style RPG that allows you to play fast and loose with all the little minutiae of day-to-day requirements for things like food, operating costs, et cetera. It also lends itself more to characters that are somewhat exceptional from the start; with less emphasis on meeting demands outside of the party's specific specialties, there's more room for a group of 4-5 players to each min/max a character who can be really good at just one or two things, while being able to cover all the important bases as a group. The result is a system that is faster, more lightweight, and more adventurous, trading the traditional detail of the tabletop for the pulp-y, dramatic action of the novels.
On their own merits, AToW and Destiny both stand on roughly equal ground- while there are some definite benefits to one or the other, a choice between the two mostly comes down to a matter of preference. A big problem for some, however, may be in attempting to run 'Mech-scale combat. Destiny's built-in abstracted vehicular combat is simplified in the extreme, to the detriment of the system. When dealing with small 'Mech vs. 'Mech engagements, it works well enough. There are much worse ways to try and resolve, say, a brief duel between two Clanners during a minor trial, but it scales very weirdly, and breaks down entirely the moment one tries to implement non-'Mech units. It's totally unfit for vehicular conflict at any sort of meaningful scale. For this reason, the book also provides conversions to Classic. However, some of these conversions can be a bit more clunky than the compatibility-oriented approach of A Time of War, making the system less-than-ideal as a complement to CBT campaigns.
So in sum, MechWarrior Destiny is ideal if you want a lightweight system that allows your players to spend more time as exceptional individuals without having to worry about the specific rigors of logistics or a wide base of often-mundane expertise. Much like authors of many BattleTech novels, GMs have more freedom to handwave things or assign target numbers and requirements arbitrarily, allowing a GM to apply some light plot armor and convenient coincidence at some times and strip it away at others so as to form a series of cohesive narrative beats. On the flipside, those looking for detailed rules and assets or streamlined compatibility with other systems may be disappointed.
Note, as I prefer more detailed campaigns, there is some minor bias present in this review.