I've got the high low on my CP so I can comment on it. However, it's the only spinner I've used in the last 15 years so I don't have a lot to compare it to.
I understand that the TTHL is top mounted, and for me won't be as aesthetically pleasing. I assume it takes a larger mounting hole than the TT2, but by how much? Does it look gawky on a CP?
I flush mounted mine (routed out some wood beneath the mounting plate and cut a hole in the plexi the same size as the plate) and it looks great.

If I went with the TTHL, would I be sacrificing anything that the TT2 would handle? Does the Energy Storage Cylinder give the TT2 a completely different feel? Does the TTHL have an Energy Storage Cylinder, or does it need one? I would like to play Arkanoid, Cameltry, Tron, Tempest, etc. and would like them to feel as authentic as possible.
I can't really comment on authenticity. If feels great, but I haven't played real spinner games in years.
I also understand that the TTHL comes preconfigured for mouse right and left click. Currently I do not have a trackball and may not use one. I also do not have a trigger joystick (Discs Of Tron) and may not add one. Would you say there is still value in the TTHL for me?
I use it with DoT, Forgotten Worlds, Zwackery, and Caliber .50 but by far I use it the most with DoT. For me, without a triggerstick, it wouldn't get near as much use. Maybe I'm misunderstanding your question, but I don't know of any trackball games you can substitute a spinner for.
I like the idea of added functionality of the push pull, but don't know if it's really something I'd use, or miss if I didn't have it.
I can't predict what your gaming habits will be, but I honestly doubt that you'd miss it unless there's a game you really want to play that needs it (like DoT is for me).
I would like to play Frontline as this used a push spinner; has anyone played this with a TTHL?
I've got mechanical rotary sticks on my cab that I use in conjunction with the GPWiz40 for Frontline and it plays great (besides the aim reset bug between lives and rounds, any progress on this Randy?). You could certainly use the TTHL in conjunction with a joystick, pushing and pulling to shoot and throw grenades (as I do with Caliber .50), and it works, but it's definitely not the best solution. Your aim can get off as you push and pull (especially pull) and it can be hard to be precise. And mechanical rotary games like Frontline don't play too amazingly well with an optical spinner anyway. Not the best soultion, but it would work.
I love the HL. It feels great and it has tremendous versatility. However, if I didn't play so much DoT, I probably wouldn't miss the upgrade from the regular TT.