The 5370B has the very good OCXO 10811 built-in, which is mandatory for stable and precise measurements.
You might upgrade the A version accordingly.
The B version has an upgraded / compacted (1 instead of 2 PCBs) µP PCB, and better Firmware. Please check both Service Manuals for comparison.
The 5370A/B is a specialized instrument for best doing T.I. measurements, 20ps single shot. Max. frequency is 100MHz, which can be resolved to 12 digits @ 10sec Gate Time (external gating).
I prefer my 5335A over my 5370B, as it's got so many more versatile measurement modes, T.I. down to 1..2ns, which is sufficient for most oscillator stability measurements. It also has 200MHz and 1.2GHz frequency inputs, which can be resolved to 10 digits @ 10 .. 12 sec Gate Time, which can be achieved by changing an internal capacitor, or by using GPIB.
It should also have the 10811 OCXO.
John Miles (KE5FX) TimeLab program supports both counters, which is a big Plus.
It really depends on your use case, which counter to chose.
Frank
PS: If you go for the 5335A, make sure it has the OCXO, the digitally controllable front end, and the C channel. Please check, which option numbers these are