I've trained in Judo quite a bit and hold dank rank in both Aikido and Jujutsu.
To be clear - what we refer to as randori in Judo is not done in most Aikido. One of the primary differences is that most Aikido schools do not engage in randori where the role of Uke and Tori/Nage does not exist, and where two people are going all out trying to get technique to work with both persons being allowed to try as much as possible to stop or counter the other.
If you want this sort of experience you have to do Shodokan Aikido which has a competitive aspect along Judo lines and has a randori method like Judo where both participants are allowed to resist and counter techniques at will at full force if necessary. I am not sure of any other Aikido method that removes the Uke/Tori relationship in this manner. The difference to Judo randori is the longer ma ai which negates the foot sweeps and hip throws, forcing one to use only joint locks, strikes and throws using total body coordination.
Of course there are many other benefits to training in Aikido outside of randori, but if you want something similar to how its done in Judo you will most likely only find it in Shodokan. Unfortunately we are not everywhere so I'd suggest you take a look at the sites given by David above - www.tomiki.org
is the best place for you to look if you are in the U.S.
I hope you find what you are looking for.