Where'd you get the sense that he was "a peer to Thrawn himself in tactics and strategies?"
The book is careful to specify that Thrawn is cultivating his innate talents in this area and that Eli is improving as a result of that interference.
Thrawn probably sent him to the Chiss as a safeguard to ensure the Chiss gained information on the Empire if he were to be killed whilst in service to the Empire.
( Post by Syndiciate )
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Thrawn saw that Vanto had a natural aptitude towards tactics and strategies, and helped him develop those abilities over the years. However, Vanto was not a "peer" to Thrawn anymore than Nightswan was. The novel made it abundantly clear that Vanto was still far inferior to Thrawn as a tactician.
As for why Thrawn sent Vanto to aid the Chiss Ascendancy, I can only assume it was for the same reasons he mentioned to Nightswan, when he offered him the same opportunity:
"There are evil things in this galaxy, Nightswan. Far more evil than the Empire, and far more dangerous to all living beings. We know of some, while of others we have heard only rumors."[...]
"But you are correct in that I wish to offer you a position," Thrawn said. "Not with the Empire, but with the Chiss Ascendancy."
"Is a human among the Chiss more implausible than a Chiss among humans?" Thrawn asked. "It would offer you the chance to stand against forces far more evil than you face now. Moreover, your work there might someday save the lives of all those who currently stand with you."
-Thrawn
IOW, there are FAR more dangerous threats in the galaxy than even the Empire, and the Chiss actively oppose them. Thrawn felt that Vanto(who Thrawn considered a 'master' tactician among humans) could be best utilized by the Ascendancy to help them fight these threats.