DOE/EASA has a tech brief which according to the table of contents addresses both subjects (efficieny during rewind and rewind vs replace). I didn't read the whole thing but you can get it at
Most repair shops aren't going to make any promises about efficiency. They usually don't have the original design/test data so they won't make any predictions or guarantees. But there are some specific items that you may be able to get some control over.
One minor point on how efficiency can be improved when rewinding an older motor.... we don't need to use a higher-conductivity metal like silver.... just more copper. This is often possible because the newer insulating materials take up less room and leave room for more copper. You can ask them to specify copper cross section per turn in their quote... and then use that as a comparative basis for selecting your rewind shop. But don't let them cheat on the groundwall or turn insulation to do it.
If you don't want to go to all that trouble, one item you can put in your spec is to not allow slot fillers. You can allow packing material for tightness but slot fillers are a missed opportunity to put in more copper. The distinction can be a little grey so you can ask that they get your approval on packing material.
If you have significantly upgraded the thermal capability of the insulation system then likely the motor will be over-cooled if the fans are unchanged. It is possible to modify the fan to trim back a little bit of the excess cooling flow (it costs power to drive the fan). But would require a lot of care since again the rewind shop is not likely intimately familiar with the cooling design. Better luck if the OEM is rewinding the motor.
Rhatcher is right on the money that you can lose efficiency during burnout of stator windings. Some things to consider putting in your spec: 1 - Max temperature of burnout should be 650F unless approved by the client. Some core materials are more sensitive than others to high temperatures.... make the shop do their homework to convince you that the temperature they propose is safe for this core. Another thing to put in your spec: If post-burnout core losses (watts per pound) exceeds incoming (before burnout) core losses by more than 5%, then the seller is responsible to repair the core such that core-losses are reduced to within 5% of incoming core losses. That will give them some incentive. Also you can spec the hotspots and change in hotspots if you want. There is also a whole lot of discussion on how core loss testing should be done (what is rated flux etc).
If efficiency is really important to you and you're willing to finance a substantial redesign anyway, you might ask 'em to consider changing the volts per turn. That is not always possible but there may be ways to rearrange the circuits to accomplish it. Higher volts-per turn generally gives better efficiency at high load (lower volts-per-turn generally gives higher efficiency at low load).
I agree with the others that in general you expect a rewound motor should be as efficient as the original. Possible core burning during rewind addressed above. Most phase-to-ground failures are relatively tame and don't cause any core damage.
I can't improve on rhatcher's response to rewind vs replace.
In large motors sometimes there is a third option for coil cutout at a fraction of the cost and time for full rewind. It will require a little engineering evaluation but often a failed coil can be cut out of a large motor with no adverse effects other than slight derating of the motor. Sometimes two other symmetrically-spaced coils need to be cutout. EPRI has a very detailed report on the subject. Our plant has had one good experience with cutout coils (worked for three years until we decided to rewind for other reasons) and one bad experience with it (cut out failed coil, failed the hi-pot on adjacent coil, cut out adjacent coil, failed surge test on another adjacent coil, lost a month, still shelled out a quarter million for a rewind).