is not the issue. The issue is the format of the video that is stored on the tape.
If the new miniDV tape camcorder is shooting in its default high definition HDV mode, the old standard definition DV format only camcorder will not be able to deal with the HDV format video. Keep in mind that HDV is 1080 horizontal lines of video resolution whereas standard definition DV is 480 horizontal lines of video resolution.
If the new miniDV tape camcorder is shooting in optionally selected standard definition DV (through the menu option selection process on the camcorder), the old standard definition, DV format only camcorder will be able to deal with the standard definition DV format video on that tape. This assumes the camcorder recorded the video at SP mode (and not LP mode).
Assuming the old standard definition DV camcorder shot the video using SP (and not LP), then the new DV/HDV camcorder should be able to deal with the tapes form the old camcorder. SP and LP are speeds at which the tape can move over the recording heads and is selectable only for DV (not HDV). Default is SP. LP allows for more recording time on a tape, but can impact video quality and is never recommended to be used. There can be issues when using different camcorder manufacturers and LP speed compatibility.
Just so you know, you really do not need the expensive "special HD tapes" for the new HDV camcorder. I've been shooting HDV for 5+ years and use the inexpensive Sony Premium tapes - $28 for an 8-pack at Fry's Electronics. Cheaper in quantities from tapestockonline... I never re-use tapes. They are the archive.
Will an old MiniDV camera be able to play new HD tapes that are shot with a new HD camera? And would a new HD MiniDV camera be expected to play tapes shot from the old non HD camera? Backward and forward compatability question here.

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic