I am a little biased because this is the system I have chosen to learn (still learning it), so take what I say with a grain of salt and definitely check out BGG for more info. There are a ton of heated comparisons with ASL there.
What I wanted from a system:
2) not hideously expensive
3) squad level tactics
At the time I was making my decision, my choices felt like ASL, Squad Leader, Lock and Load, Panzer Grenadier, and Advanced Tobruk System (ATS). After reading up on Lock and Load, I ruled it out. Panzer Grenadier isn't quite the right scale (but it's rather easy to pick up for the grognard). Squad Leader was great with its programmed instruction and I messed with that and Cross of Iron. Really enjoyed it. Thought, what the hell, lets try some ASL and made the jump blindly. Bad decision on my part. I think the same can be said of wanting to make the jump from ASL from the starter kits. The starter kits feel like a great placement for the original Squad Leader, but jumping to ASL is still a monstrously huge jump. The starter kits may introduce you to the very basics of ASL, but that's it. There's no intermediary step there. While I was listening to an ASL podcast from two fairly longterm players, I realized they spent a hell of a lot of time with their noses in the rulebooks or realizing after the fact that they forgot something. For a true ASLer, I understand that's part of the appeal. It wasn't for me.
I looked into ATS, saw that every box was its own complete game. I saw they had a basic intro kit as well as an intermediate kit. I saw that the full game had a 60 page rulebook while still maintaining enough tactical detail. The more I read, the more I realized ATS was the compromise I wanted between playability and depth.
I haven't played a ton, I can in no way answer questions in detail about this or that, but I will say that what I've played, I enjoyed and I didn't get overwhelmed. I am a fan of ATS, and I feel like it fills some of the space between ATS starter kits and the full crushing weight of ASL. Anyway, hope you find a good fit with a system. These kinds of games are a blast to play.