I trained aikido for quite a while years ago, and I train BJJ now. I really enjoyed aikido, but I was a cop at the time and didn't have any delusions as to it being "effective" in a fight. Maybe a wristlock or two for control but that's it. I quit training when I ended up moving.
That said, the ukemi was the best thing about aikido. Being able to fall safely in any direction saved me countless times, the occasional trip, falling on ice, mountain biking crashes, and now in BJJ.
The compliance was something that I had to overcome when I started jiu-jitsu. If someone wanted to sweep me, my aikido background would say "ok, let's roll that way". I'm still fighting with it (still a BJJ newbie ~8 months or so).
My attitude hasn't really changed much. As a self-defense system mainstream aikido (aikikai) is shit. It isn't realistic and is focused on responding to largely sword-based stylized attacks. These were the teachings of the founder, and it's been passed on that way. The biggest problems I saw were that as someone gets more experienced doing aikido, uke tends to "read" the intentions of nage and fall the way they are supposed to at the very basic initiation of force on the part of nage. So uke goes in for a straight punch, nage sets up for a kotegaeshi wrist lock, which uke has done thousands of times, and uke does the appropriate ukemi for kotegaeshi as soon as the wrist is turned.
Here's an example of what I mean:
Intermediate Aikido: Mune Tsuki Kotegaeshi - YouTube
I always felt that the best example of aikido was when you were paired with a rank newbie. They don't tend to "move" like an experienced uke does and often times you get the reaction that alot of folks in this thread have talked about.
1) Grab my wrist.
2) No like this.
3) No don't let go when I do the technique.
Which is a valid reaction for a BJJ guy (hell no you aren't doing that to me, I'm resisting!) but really is sort of what aikido is all about. In the aikido mindset, if you let go of my wrist, you are no longer attacking my wrist. Problem solved (until I get punched, but you know what I mean). Aikido is ENTIRELY defensive. The only thing that is even remotely offensive is the idea of atemi (strike) after someone has initiated an attack as a distraction.
The aikido-based systems that incorporate aspects of other training methods (live sparring, resistance, etc) are marginally better, but still involve virtually no ground fighting, so even a basic BJJ guy with good takedowns is going to own an aikidoka IMO. The art just isn't built to address it.
Unfortunately, I think a large part of the delusion that aikido is effective self-defense comes from Segal movies. I know SO many people that got into it because of him.
But I agree with the other poster that said aikido is fun. It's a blast. And working with a high level aikido guy is fun too, as long as you are playing by aikido rules. a 4th Dan or so's ability to play with momentum is really interesting. But it's not self-defense. There are some useful nuggets in aikido, but it is definitely on the flowery side of the martial arts spectrum.