Lots of things affect how long it takes to rip a DVD. To get meaningful information it is necessary to compare like with like!
Is the same DVD being used on each machine?
Is the same transcoding program being used on both machines? The same codec? The same audio settings? With the same final video quality settings? For example, the one that seems "faster" could be doing a plain-vanilla one pass encode at a lower bitrate and PCM audio and the one that seems "slower" might be making a creditable job of a multipass higher bitrate encode with a bunch of filters enabled and mp3 audio.
I use Handbrake for this task and I can use among others, these filters: De-telecine, Decomb, Deinterlace, Denoise and Deblock and they can drastically increase encoding time compared to a plain ordinary "good enough for my TV and eyesight" encode. Also there are a whole bunch of settings in an "Advanced" section I haven't even touched.
Once you know the same job is being done on both machines, if you still have a speed anomaly I would think about the drives used. If both machines have separate reading and writing drives, check speed settings and disk compatibility and see how fast the burn drives are running.
The newer read drive could have Riplock in the firmware which slows the data transfer rate when reading DVD-Video data - usually a drive capable of 8x or 16x read speeds would drop to 2x or 4x. It does not prevent ripping however, just makes it less convenient. In some cases, firmware flashing is all that is needed to remove this feature from a DVD Drive. On some models pressing the eject button a certain way for a certain time cuts out Riplock. Ripping forums are full of - often quite specific- information about this sort of thing. Makers say it is to make machines run quiet, but some allege it is an MPAA initiative. Even if the slow machine's drive doesn't have Riplock, there may be settings in the encoding program that are limiting the read speed to keep the job quiet.
One way to isolate the problem would be to first rip the same DVD to a VIDEO_TS folder on the hard drive of each PC and then use these as input for identical encode tasks, output being to hard drive folders. That way you are comparing computing performance and cutting out the optical drives.