You may also want to read some SCSI app notes to be sure these two standards are interchangeable - IIRC 50-pin connectors were for regular SCSI (8-bit) and 68-pin were used in Ultra-SCSI (8-bit, but faster) or Ultra-Wide SCSI (faster 16-bit). One that briefly talks about the differences is SLLA035 and another is this webpage from Adaptec.
The 50 pin are "narrow" or just plain SCSI, 8-bit bus.
The 68 pin are "wide", 16-bit bus.
Either can operate at normal (5 MHz), fast (10 MHz), or Ultra (20 MHz) synchronous speeds, or asynchronous. The 68 pin may also be differential (incompatible with everything else) or LVD (compatible with everything except old school differential). Differential is uncommon but LVD is very common. This was used starting with Ultra2, U160, and U320 (40, 80 and 160 MHz respectively, giving 80, 160, and 320 MB/s speeds). AFAIK, all U2/U160/U320 controllers and devices will fall back to normal Ultra speeds without LVD signalling if inter-connected with such devices. There is an issue of termination: Few if any LVD devices has internal termination and depend on a separate active terminator at the end of the cable. By contrast most single-ended (non LVD) devices have built-in selectable termination. Termination is NOT optional. I suspect that the OP's issue is caused not by the adapter but by the new drive's lack of built-in termination which the original drive almost definitely had.