If you ask 100 different people you'll get 100 different opinions on schools in Tyler. I can honestly say I could identify friends/neighbors who have had both positive or negative experiences with essentially every private school and all the public schools my kids would feed through. It comes down to what's best for your kids/family. I get the impression from your initial post public schools will suit you just fine here, but the private schools are worth a peek if its financially feasible.
My perception is that if you're looking in the Legacy attendance area, I think you will not find any issues with public schools that would be out of the ordinary from what you may find in your present location in DFW. Tyler is fairly segregated geographically, though the schools are zoned in such a way that the schools in the Legacy attendance area are certainly not homogenous. The facilities are or will be all "new" (within last 20 years) from elementary to high school. Legacy and Tyler High are both just a couple years old and are impressive facilities. Of course, facilities are just one component. I'd encourage scheduling a tour of multiple schools and checking them out. May be hard with the year about to end, but do it while students are there, if possible.
We are moving our young kids from private to public next year, and it was not a decision taken lightly, but we have "faith" in the schools our kids are zoned to attend and in the present trajectory of the district. TISD's recent past is not stellar, and there has been a drain of folks to the private schools. I think that has zapped the public schools of families that would otherwise be involved and engaged--nothing against having your kids in private school at all. My perception is that TISD has made a lot of strides in the last decade to overcome that and other challenges.
If you have concerns about public school curriculum, want your kids to get a faith-based education, want to make sure your kids get to participate in any activity regardless of "aptitude," smaller class sizes, etc., then there are a number of solid private schools to choose from with different "brands" based on your kids' interests and your families' religious preferences (if any). With that in mind, some of the private schools have a better reputation than others in terms of inclusion, and if you're not from Tyler you may find some folks here may not really care to get to know you or your kids, which may be something to consider for their social lives. I can elaborate on that via PM if you're interested.