The original edition of Robotech was a game I played a lot, but would have trouble playing now.
The Palladium 'house system' is very clunky. It appears to have begun life as a D&D (1st edition, maybe pre-
AD&D) clone, and generally didn't add much to it other than a bit more interesting combat system (a core mechanic, as I remember, is that characters earn 'parrys' and such per level that they can choose to use to block attacks. It's a bit more dynamic than the basic D&D metaphor of combatants taking turns slugging it out.
Characters advance slowly, and at different rates (a technician has a different experience point chart than a fighter jock, for example). An issue in Robotech is that the designers didn't really think about making a useful party, so there's 1 'Fighter Pilot' class, 1 Destroid Pilot, an Engineer, etc. If you're doing a campaign based off the SDF-1's voyage, for example, there's a big incentive for the players to almost all be 'Pilots' as they get to regularly do stuff. You might have one or two that take other roles: maybe someone really wants to play a mechanic or a bridge bunny. Still, these characters better bring something to do during fight scenes.
This can be moderated a bit by doing more interesting adventures, such as maybe having the player characters all be friends and be involved in some sort of conflict that is outside normal military scope. Maybe investigating some sort of weirdness that higher-ups don't believe, or some traitor who happens to have a grudge against all of them. Classes are very focused, generally.
Still, had it been my choice, I would have wanted several Pilot classes based of anime stereotypes (Which, for the record, are pretty much the same as the stereotypes from a lot of other genres as well): The Ace Pilot (Maybe gets bonuses to "Save the Girl"), the Wingman (Bonuses to set up shots: think someone who's special ability is making everyone else work better), the techy Pilot (fixes stuff, etc.)... and so on and so on. Basically, have a bunch of classes that can work together.
Combat is a bit slow by modern
RPG standards. Sturdy but not exciting initiative system, and characters get more attacks as they advance down various martial arts paths. Mecha combat is a subset of this, and there's minimal rules for chases and such.
The Mecha have massive amounts of 'MDC' or 'Mega Damage Capacity.' 1 MDC is equal to 100 SDC. A normal human would have a few hit points (representing serious damage) and a couple dozen SDC. So, therefore, being hit by a military-grade weapon is generally lethal damage to an unarmored human. This really isn't dealt with.
Some really hate the MDC system and play by either multiplying it out (so mecha have hundreds or thousands of SDC) or finding other alternatives. I didn't mind it much, but it had some definite flaws: MDC handheld weapons (common in the
SC and Invid eras) meant it was common for characters to be running around with weapons that could destroy buildings with a few shots, and really reinforced the old-fashioned 'Sleep with their armor on' mentality of 80s role playing.
I feel the game failed at genre emulation. In the cartoon, Veritechs and Battle Pods are fragile and a failed dodge often means the pilot had better hope they can eject (Oops, I don't think battle pods have ejection seats!

). The game gives out enough MDC to mecha that most can take several hits from the opponent's main guns without a problem.
A possible solution to this is that the Mecha are divided into components: body, head, limbs, and perhaps a few other zones. However, it's still difficult to take off a limb or weapon with a good shot, so these rarely got used. There were some tables to add random lcoations in, but they weren't comrehensive and slowed the game further.
A common complaint about the system is some spot rules for shooting down missiles. This is another opportunity to mimic the feel of the source material, as several characters shoot down missiles at various times. Unfortunately, you can't, as the system explicitly limits the number that can be shot down.
So, as a result, combat is a bit slow and doesn't feel like the dogfight it should be.
Outside of combat things don't get much better. Characters have skills, which are rated in percentiles. Skills are granted by class, with a few skill selections available for meager personalization. Skills get a percentage as a base number (So if you have Pilot, you might get a free 30% in it) and then a bonus per level (say +3%)... Every level, the skills need to be recalculated, and there's nothing really interesting about them other than numbers going up.
Some skills are most definitely 'better' than others unless the group is hard-core role-players who really avoid combat. If I remember correctly, Boxing is a no-brainer skill, as it adds attacks and a raises the character's strength!
Using skills is a relatively simple affair of rolling under the percentage. It works, but is not particularly innovative.
There is also attributes that can be rolled under. So, sometimes you need to roll d100 and try to get under a percentage, sometimes you roll
d20 to get under a smaller number (usually 3-18).
This review is for the previous edition. I've heard the new is a reasonably good guide to the series, but uses a tweaked version of the system with few of the flaws fixed. Mecha have less MDC, but many weapons do less damage.