Well I can't really say much more. Tai Chi has very similar techniques (ikkyo, nikkyo, etc even zenponage/sumi-otoshi), as do many martial arts. Push hands involves having contact (wrist to wrist) and moving the contact point around in a circle. Each of you feel when the other either over extends themselves or withdraws too much. This can results in ikkyo, kokyu-nage or other techniques. Also, although tai-chi people often move their hips more in an up and down direction, and sometimes use a 'whipping' motion with their hands, everything is generated and controlled by their centre. Also, even for punching, the arms must be relaxed (until the final point of contact). This increases speed and response. Of course, just like Aikido, much of tai-chi is now orientated around 'excercise' and therefore people go through the movements with little or no control of their hands by their centre.
In some ways I think Aikido has regained aspects of Chinese martial arts which alot of Japanese martial arts have lost (relaxation, centering, moving with the person).
An example from writings on Tai Chi :
"When he puts pressure on or attacks us in one direction, rather than resisting the pressure or the attack, we
confront him with the Void by either diverting his force away from us or by removing ourselves from the path of his
force and then attempt to counter attack him as he is unbalanced.
Being still higher or lower than the opponent means that if his force is upward directed we direct it even further
upward, likewise if it is downward directed we direct it yet further down."