Most ATOW skills, abilities, etc don't work with Alpha Strike (dealing with individual weapons, or piloting skill rolls,etc). The Special Pilot Abilities from ATOW were converted to AS in the Alpha Strike Companion.
You could certainly have an ATOW role-playing game, and then use Alpha Strike for "mech scale" combat in order to resolve quicker, but a lot of ATOW would get "lost" in Alpha Strike.
AS Companion:
New standard rules: A section of the AS Companion is effectively errata to the standard rulebook (and now available in the 2nd printing the AS rulebook). Variable movement modifiers, Minimal Damage, Occupying/Intervening Terrain, Rear Special Ability, Battlefield Intelligence, new PV system.
Optional rules: ASC has a bunch of optional rules to tweak gameplay. Variable Damage, Lance/Star Movement, Critical Success/Failure, additional artillery options, Fortified Positions, Advanced Buildings, Engine Explosions.
New Unit Types: Drones/Robots, Tripods, Superheavy Mechs, LAMs, Quadvees.
Force Building: Special Command Abilities, Unit Roles, Special Pilot Abilties, Formations. I lump these all together, though its certainly possible to use some of them separately. These gives game options over what just the unit has. So the type of Lance, the pilot and the overall force specializations all give different options to a player beyond just what units do you have. This section is then crucial to the Combat Manual series.
Abstract Space Combat: blowing up stuff in space with fighters up to warships.
Alpha Strike Conversions: the rules for converting BattleTech units to get their AS stats. (This section requires no other BT books to convert from a unit's Technical Readout entry or Record Sheet).
Scenarios for Alpha Strike
Expanded Repair and Salvage Rules
Combat Manual: Mercenaries
Part of a new series. Combat Manuals gives rules for creating a "faction flavored" force in the Late Succession Wars (3010s) to Early Clan Invasion (3054). Which units are available, what command abilities different regiments have, any force building restrictions (no infantry, only heavy 'mechs, etc), and unique pilots. Each has new formation types and new command abilities as well. And there is a mini Technical Readout featuring the new artwork for some classic 'mechs (ie. former Unseen). Mercenaries is the first in the series.