Let's start with first impressions. I initially hated Birdy's character design. None of it made much sense, from the weird high-heeled outfit that I guess is like part of her skin, with kind of ugly color schemes, to her alter-ego as a ditsy pin-up model. Also, within the context of the rest of the show, the main gimmick of a high school boy having to share bodies with a rockin super-agent alien babe really makes no sense and has little bearing on the main plot and action. Lots of people die over the course of this anime, and you're telling me that Tsutomu is the only one lucky/special enough to be saved in this way, not once but twice? The other weird thing is that no other humans know anything about aliens, and yet the aliens don't seem to care about hiding even the slightest detail from Tsutomu, as if they had planned having him be inside Birdy from the start. This anime not only doesn't need the Tsutomu gimmick, I think it would be better without it, to be honest.
I could go on and on about how various plot details/elements/devices don't make one lick of sense, even for anime, but I'm going to move on to what I actually did like about this anime. While Birdy's character design was off-putting to me at first, I grew to appreciate it more because of the consistently outstanding character designs everywhere else. The humans are wonderfully unique with a lot of personality, and the alien diversity, while cliche, is pretty good, similar to MIB or Star Wars. The CGI interspersed throughout was decent, but the non-CGI animation was some of the best I've seen in an anime. Every scene has multiple moving elements with hardly any reused stills that are noticeable. There are constantly changing perspectives, and character motions are very fluid with lots of little details that I really appreciated. For instance, on the train, the scene shakes and the characters jostle occasionally. That's a lot of extra animation work for a basic scene. Or when the characters are running and they turn a corner, the hair will sway in a natural way, and you'll see multiple angles of the characters as they turn. This attention to detail in the animation really pays-off during the action scenes. The fight scenes, especially in the second season, are epic (from an animation stand-point).
Besides the animation, the voice acting was top-notch, the music and sound were spot-on, and the production values in general were very high. If the plot was a little bit smarter and more interesting and the fictional universe wasn't so inconsistent, I would have given this 5 stars. But it's a strong 4 stars, and for those of you who don't mind things not making sense, it might be 5 stars for you.