The standard engine is a Rolls Royce Nene, as fitted to the Canadair T-33/CT-133. The alternative engine is the original Allison J33-A35 fitted to US-built T-33s.
The biggest difference is that the Allison has a significant delay in thrust response when you advance the throttle (up to 15 seconds to spool completely up), making it more challenging to manage power during approaches. Overall thrust is similar (5,200 lbs for the Nene, 5,400 with water injection for the Allison) and the spool-up response is the biggest operational difference.
Interesting side-note: The Nene was built under license by Pratt & Whitney as the J42, which powered the Grumman Panther, and was reverse engineered by the Soviets who used a modified illegal copy to power the MiG-15.