Oro, you stated...
On general Nelson Miles, if you study his campaign you may be impressed. He was more relentless than Crook or any of his predecessors, and his innovative use of heliograph signal stations allowed for faster communications for his forces.
I've spent the last few years reading everything I can find regarding the Apache Wars, so I've definitely studied Miles and his 5 month campaign against the Chiricahua. I come away unimpressed with Miles in every respect except one - he did and said whatever he could (including blatant lies) to put an end to the last of the "renegade" Apache. It's something Crook could have and one could argue that as purely a military man he should have done rather than put his trust in the renegades to live up to their word and come in on their own.
Here are some of the things Miles did in the last 5 months of the Apache wars.
1. Miles (along with Sheridan) distrusted the Apache scouts that Crook relied on to track and constantly harass the renegades, so Miles took the majority of them out of service. If you want to talk about impressive strategies, I would argue that Crook's understanding of the Apache allowed him to put Apache scouts into service and I personally agree with his assessment that "Chricahua scouts were of more value in hunting down and compelling the surrender of the renegades than all other troops engaged in operations against them, combined."
2. The employment of the heliograph system was indeed a novel approach for communication and worthy of some credit, however in the end I found no evidence that it's use ever allowed his soldiers in the field to find Geronimo and his band.
3. Miles received 2000 additional soldiers giving him a total of ~5000 men (1/4 of the US army at that time) to try to find, fight and capture Geronimo and his band. The Mexican army also had thousands of soldiers out looking plus the additional volunteers and assorted bounty hunters, etc... amounted to something on the order of 9-11,000 people out looking for 18 renegade warriors, 13 women and 6 children. Other than 1 time where Lawton came across a camp in the Sierra Madre, Miles' campaign never captured or killed a single Chiricahua.
4. Miles eventually came to appreciate Crook's use of Chiricahua scouts. He asked for advice and assigned Kayitah and Martine to accompany Gatewood on a mission in the hope that with a smaller force and the use of the scouts he could make contact with Geronimo. Gatewood was eventually successful with the help of his 2 Chiricahua scouts and George Wratten as a trusted interpreter and they convinced Geronimo and the last of his band to surrender.
In military reports, Lawton took credit for the capture claiming that Gatewood "failed to secure a surrender" and that Lawton himself was the one who finally persuaded Geronimo to come in. Miles listed all the officers who had served with honor during the 5 month campaign but failed to ever even mention Gatewood's name, and Kayitah and Martine (who it can be argued were the most important 2 men without whom Geronimo and his band would likely have continued evading the troops) were subsequently put on a train and shipped to Florida with the rest of the "hostiles."
In short, I see very little impressive about Miles' "campaign" against the Apache. He was in the right place at the right time imho and despite himself he happened to be in charge when the last of the renegades came in. I don't see anywhere how he was more relentless than Crook and his forces.
As to what sort of soldier or indian fighter Crook was, that doesn't enter into my argument at all. I have little or no knowledge of what he did or didn't do in other wars, only what he accomplished in the Apache Wars of AZ, NM and Mexico. I'm not oblivious to his faults at all, I just don't believe personally that Miles did anything outstanding or impressive to end the war of attrition against the Chiricahua, and his lack of credit to those men who did the "dirty work" leaves me with a very bad taste.