Anime

So, I watched Evangelion but basically none of the others you mentioned. I feel like such a fraud as a moderator of [email protected], but in any case, I can recommend at least one mecha series that I particularly enjoyed. It is more a parody of the genre, but sometimes its through parody that we realize the best that a genre has to offer. Specifically, Brave Bang Bravern!.

Is Bravern a comedy? Yes. Is Bravern a tragedy? Yes. Is Bravern a romance? Yes. Is Bravern kick ass? Hell yes. It's hard to put it in a box since it will pull some new weapon out of nowhere and break out as soon as you try. At one point, the giant, sentient robot was building giant robot-sized gunpla, and this was just accepted as normal and never commented on by any of the characters. It's an absurd take on the mecha genre that simultaneously shows an absolute love and dedication to what makes it great. The genre might be about big robots, but it is the human connection that makes us care about the story at the end of the day.

tl;dr - Watch Bravern

I don't have much to add, but seconding Bravern, it's really that good.

The thing to keep in mind about 86 is that it's a very grimdark kind of show (themes of racism, lots of character death). It's a good show and worth trying, but if grimdark isn't your thing, don't be surprised if you bounce.

Hmm . . . so what else has no one recommended yet that's worth trying. Gargantia on the Verdurous Planet, of course. You might find the earlier installments in the Aquarion franchise (Genesis of Aquarion, Aquarion EVOL, and Aquarion Logos) somewhat amusing—they're more on the silly side, but so are some of the shows you listed (the first series especially has some very silly-weird stuff, like the episode where the characters are cosplaying each other).

Older shows that you haven't mentioned and might be worth looking at would include Patlabor and Escaflowne.

And as someone has already said, do finish Gurren Lagann—it's worth it.

Are there good modern mecha anime that match older anime like Super Dimension Fortress Macross or Neon Genesis Evangelion?

I'm having a hard time with this because I don't think those shows even matched each other. What is it you liked about them that you don't like about some of the newer stuff you've mentioned?

I loved the first season of Aldnoah Zero

It's realistic mecha, e.g. Patlabor, using believable science to fight science fantasy mecha with un-realistic abilities powered by "Aldnoah" a magical/"sufficiently advanced technology" power source discovered on Mars.

Don't bother with the 2nd season though, they lost the head plot writer Gen Urobochi it the writing really suffered.

If you like 80s anime and hordes of polygonal ships flying around fighting each other, there's Legend Of The Galactic Heroes: Die Neue These, a remake of the long running 80s TV and OVA series.

If you like big things fighting each other, there's SSSS.Gridman. Technically the titular figure is a mech, but it's a take on a mostly-forgotten Tsuburaya tokusatsu show.

And, as someone else said, definitely finish Gurren Lagann

Attack on Titan (flesh mechas)

Code Geass

FLCL

86: I highly recommend it. It's more cerebral and introspective without being pretentious.

Do yourself a favor and checkout Gunbuster (1988) and its loose sequel Diebuster (2004). Gunbuster was directed by Evangelion director Hideaki Anno (and it might be his most concise stand-alone work), while Diebuster was directed by his protege, FLCL director Kazuya Tsurumaki.

Both are just 6 episodes, with fantastic Gainax animation, great soundtracks, and masterful storytelling. I strongly recommend watching the original Gunbuster before Diebuster, though it isn't totally necessary.

I know it may be a hot take, but I am not personally a fan of Gundam. Which seems like a perfect fit but for whatever reason every time I have tried to watch it I just never make it more than a few episodes in.

As someone who is in the process of catching up on all things Gundam before seeing GQuuuuuux (the new Gundam by the creators of FLCL, Diebuster and Evangelion) later this month, I highly recommend giving it another try and sticking with it until at least the second half of the original Mobile Suit Gundam (0079). There are a couple reasons for this:

• The back half of Mobile Suit Gundam is significantly better than the front half, and while the ending is a little bit rushed (the show got cancelled, or something like that), there are a lot of really nice Macross and Evangelion-esque concepts that come into it. Gundam really is significant to the history of anime in general and the mecha genre, and by the time I got to the end of it I finally understood why.
• Watching the original Gundam makes watching Zeta Gundam (the direct sequel) much better, and it's a show that build upon the lore and characters of the original in a fantastic way. I know it's a big ask to suggest that someone watch a 50 episode show in order to watch another (arguably even better) 50 episode show, but Zeta is truly a 1980s anime masterpiece in the same way that Eva is a 1990s anime masterpiece.
• If you ever watch the early Bones mecha anime Eureka Seven, which is pretty good in its own right, you'll be amazed at how much it parallels the story and character development of the original Mobile Suit Gundam.

Gurren Lagann (It seemed okay but I never finished it)

There are a couple of rough episodes in the first half, but I love this show and recommend seeing it through. This is a show where the scale and scope of the story just snowballs into something really big and cool.

Finally, have you watched the SDF Macross movie retelling, Do You Remember Love? Because if not, it's fantastic and worth seeing.