welcome - sorry for having to deal with a CCL tare.
There is no magic answer, just what works best for you and your dog. Have things improved at all with conservative management (i.e. no surgery)? are you diligent about her activity and physio? Was there a plan for a re-check to see how things are going? I believe my surgeon said with conservative management you do it like 5-6 months then see if things have improved (ex: is the scar tissue supporting the joint more?). If not then one may want to consider other options. If things ARE improving it can take another 6 months to finish the process. It's long. Did that particular doctor hvae a lot of experience with CCL injuries? what were her stats on how often that worked? why did she think your partiuclar dog didn't need surgery?
Were both just vets or did you consult with an ortho specialist (not just someone who is a surgeon but an ortho specialist).
Extra Capular is a type of fix for CCL. they use some king of wire to "re created" a ligament around the knee. More common in small dogs or older/less mobile large dogs. But the Tightrope (specifically) from what my specialist explained had great stats. it's a SPECIFIC type of surgery fix. But some larger dogs do well with any extra capular it depends on the dog and the case (and the surgeon and the after care and goals post surgery).
TPLO is one of the "bone cutting" surgeries. It's probably the most common now. It's quick and easy to a practiced surgeon. thinking about it makes my stomach turn :P The other similar surgeries are TTA and TTO.
My 45 or so pound mix tore he CCL and we opted for TPLO fairly quiclky after evaluating the options. Mostly due to how badly she was doing on her knee and how active and young she was. The post right under yours by Abulafia is about her ongoing journey post TPLO (and you can search her others posts below).
If you go the surgery route, find a qualified ortho specialist and one that is practiced in the type of surgery you pick (some do only one type).
There are two members who are currently going thru TPLO surgeries as well.
Your Stories and Information About Labs with Cranial Cruciate Ligament (CCL) Tears
Cranial Cruciate Ligament Disease | ACVS