A Time of War is meant for creating and using individual characters in a campaign setting. These can be used for human-scale campaigns, or can be mated with Classic BattleTech to run CBT campaigns with more detailed pilots, command staff, etc.
Between the two currently-supported systems, A Time of War embraces the crunchy rules and unforgiving lethality that BattleTech is often known for. It's a very in-depth system that can take a while to learn, and requires a lot of work in setting up scenarios and campaigns, but in return can give much more detailed and authentic results for GMs and players willing to explore its depth. Some GMs and players may find the depth overwhelming, however, and some of the rules and procedures can at times take a little bit to grasp.
As a direct descendant of CBTRPG, and in turn MechWarrior 3e, A Time of War is designed to plug into Classic BattleTech as seamlessly as possible, with minimal stat conversions required (barring things like infantry weapons, though most of those are already pre-converted). Many AToW-exclusive rules can, with with fairly minimal handwaving, be converted for use with Classic, and vice versa. Many aspects, such as Special Pilot Abilities, are implicitly shared between the two. For conflicts that don't quite reach the scale of CBT, but still require more than what can smoothly be run one character at a time, AToW also includes the Tactical Combat system, a descendant of BattleTroops, which is designed to run combat with a handful of squads and light armored units. Opinions on Tactical Combat are mixed, but when applied correctly it can produce satisfying results.
All in all, A Time of War is ideal if you want a highly detailed and grounded BattleTech campaign with several complex options, that can easily plug in to existing tabletop rules with a mostly-seamless transition between interpersonal intrigue and 'Mech-scale combat.