Will the old ships with the old radar be dead weight in comparison, then?
Not really. The older radar worked so well. It was first introduced on the Type 052B, then went on the Type 052C, the 051C, the Type 054, the 054A, the 052D, the Liaoning, the Shandong, the Type 071, and even on the Type 051B refit and the Sovremenny refits. It must have gone many version improvements underneath and in the back end. It's sheer ubiquity and long life in the PLAN underlines it's technical success. The PLAN would not be making this in large numbers, used in so many ships and over a long period of time if the radar isn't successful.
The Type 056 and 056A appears to have a modified model of it, and it wasn't until the Type 055 that the PLAN replaced it with something else although it was a four faced fixed AESA for this ship, but one that is too expensive and too heavy. The lighter the radar the higher you can put it on top of a mast which increases the radar horizon, and a dual faced radar will obviously have less weight than a four faced one.
The Type 364 radar has a rotational speed of the antenna, which is 1 rotation every second. This means the radar has a full 360 update every second or 60 times per minute. It is optimized against sea clutter, which can be a problem with longer frequency search radars, including the Type 346 S-band radars. For this reason, the radar is responsible for the queuing of the HQ-10 and Type 730/1130 CIWS.