In my book, Judo and Aikido follow very similar, if not the same principles applied to different combative distances (ma ai).
Have done some Judo and BJJ as well. To me, there is a very easy and logical flow from standing Aikido techs to standing Judo into Judo ne waza (floor grappling). One can easily move back and forth among them depending on the situation in my experience.
If you are looking for something to complement your Aikido with floor grappling and a knowledge of non-aikido type throws and pins, I would recommend Judo. Not to mention, the balance breaking and combination knowledge gained from Judo randori is a major aid to applying Aikido techs and making things effective.
For an Aikidoka I'd recommend the Judo over BJJ, since in Aikido our main area of operation is standing up. BJJ tends to want to get you to the ground to grapple you into submission on the floor, even if you begin the encounter from standing.
Honestly, I think if you are in control from a standing position (which is our aim in Aikido), why risk going to the ground and then trying to establish a superior position to apply tech? For the ground work, the BJJ is great, but I've seen nothing that makes it that different from skillfully applied Judo.
It depends on what you are looking for as said earlier. To a person not inclined to either one, I'd say try both. But having tried both BJJ and Judo, I prefer the Judo. Just blends better with the Aikido I do, which was founded by a high ranking Judoka and Aikidoka.
Check out the dojos, do some classes, see what feels best before you decide. In my book, certain people are predisposed to certain types of martial arts, psychologically and otherwise.
To be an effective fighter though, master the 3 basic realms of unarmed combat - standup striking, standup locking/throwing and floor grappling.
Hope this helps.