Several factors. I have to disagree with some of the previous answers.
Shaft length and diameter unless you want to change sheaves. Keyway dimensions can differ. Some motor shafts can be bushed.
Mounts are usually much easier. Even to get an AX series belt on my Ridgid, I had to put a spacer on the mount. Darn Chinese are not very good at translating either "effective length" or "outer length" specs, A bit of plywood makes a perfectly good motor mount. If the tension is by gravity, you may need to add weight or a spring to make equivalent as older motors tended to be heavier. As with all belt drives, you set by belt deflection force. ( or snug until it does not vibrate)
Keep the RPM the same unless you want to change sheaves. But be forewarned, most wood working machines already have diameters too small for the belt specifications. Minimum diameter for HP is specified by the surface area for contact. Go to Gates or Continental WEB sites for design data. If your cutter head has a single 2 inch diameter groove, it won't support much more than 1 HP by belt spec.
Going from a 1725 to a 3450 to save a few bucks gets overcome by sheave size and cost.
A 1 1/2 HP motor seems a tad small for a 12 incher but only you know how it preformed. 3 HP probably means twin belts at least ( many 3 HP tools run 3) , but not sure if the spindle on the head can accept a wider sheave. So, look at the specs, look at the parts. If it is already double, I would go ahead and slap in a 3 HP. You can increase the tension to increase total friction ( coefficient x force) but at the risk to undue stress on bearings.
Motor prices do differ hugely. Bearing quality, overall quality, duty cycle.
Just because it is a TEFC does not tell you how well it dissipates heat. What duty cycle are you willing to pay for? If a production shop with automatic feeders running all day under full load is very different that running a board, picking up another etc. as it cools down between boards. Good motors wil provide specs. Cheap ones won't.
Quality sheaves can cost a lot more than the difference between motor speeds.
Good motors rate HP on what is delivered to the load under standard conditions. Cheap ones may rate on power consumed. Universal motors are often rated as "equivalent" based on power, not load.
So, what are you working with?
What is the motor RPM
What are the two sheave diameters?
Single or multiple belts?
Are the shafts long enough for more grooves ( highly doubtful)
Simple on/off switch? So internal thermal protection or not?
Face frame of H frame mount?
For reference, look at offerings from Leeson, Baldor, Dayton and MCS. That should give you a good idea on prices and features. Internal thermal protection, or load/time protection in a magnetic starter switch? Prices can run from $350 to $1300 for a 1.5HP. Maybe you can get away with 2HP, but not a big difference.
To be technical, a pulley is a machine containing a sheave on an axle in a housing to transfer force. A sheave is just the round part.