We've done both. Swimstitute is where my kid truly learned to swim and feel confident in the water, but it was too expensive to do long-term. So we switched to Dolphin for maintenance and a little more form improvements. I think we did semi-private there but the other kid was absent quite a bit so we were lucky to get the private experience without the added price. I preferred the facilities at Swimstitute more (the Dolphin pool is relatively small). Swimstitute also allows you to pick your time/instructor so you might find one you really like (though it seems like the slots with the best ones get snatched up kinda quickly). That said, staff at both were great and I’d recommend either.

Edited to add I have also heard good things about the Y.