The primary difference between discrimination on the two Tesoro's and the Minelab's you mentioned is the fact that Tesoro uses variable discrimination and the Minelabs use notch discrimination. In other words, if you set your discrimination to a specific level, the detector will reject all targets at and below that level of conductivity. Notch discrimination allows you to reject any notch or group of notches, and accept all others. Regardless of whether they represent targets with conductive values less than or greater than those you set to reject. That fact alone will reduce the amount of trash (or at least increase the amount of goodies) you dig with the Minelabs.
Of the four Minelab's you mentioned, I currently own both the E-TRAC and the X-TERRA 705 for two reasons....... the Explorer and Safari are not as well balanced as the E-TRAC due to the E-TRAC having a 13 degree offset in the grip. As I've gotten older, I find I can hunt much longer with a better balanced detector. Between the Safari and the Explorer...... the Explorer (and E-TRAC) provide both ferrous values and conductive values. Not to put down the Safari, because it is a good detector. But why spend all that money when, for a few hundred more, you could have both ferrous and conductive TID simultaneously? Based on the ergonomics, I chose the E-TRAC over the Explorer. As a side note......if detector balance is an issue (and you will find that the Explorer, Safari and E-TRAC are much heavier than the Tesoro's you're now using) The X-705 is better balanced and lighter weight than the other Minelabs you mentioned.
For the type of hunting you indicated you do, either the Explorer, E-TRAC or X-705 will serve your needs. The slower sweep speed typically associated with the Explorer and E-TRAC, compared to the X-TERRA, will allow you to "cover more ground" in a given period of time, with the X-TERRA. The X-TERRA 705 has a Beach tracking mode and will allow you to maintain optimum ground balance on those Florida beaches you hit each year. For the parks and yards, you can set the GB automatically or put it in tracking. On the other hand, the E-TRAC doesn't require any ground balance at all, as the software takes care of it for you.
Dollar for dollar, there is a big difference in price between the E-TRAC and 705. And if you are like many of us, one coil just don't cut it! Something to consider is to buy the X-705 and use some of the money you saved on an extra coil or two. If you get the Gold pack, you already have an elliptical HF coil for the beach. Just make sure you put some silicon around the coil cover and cable entry point as it is considered water resistant, not waterproof. If you have the opportunity to buy the 705 with your choice of coils, you might consider getting the 10 inch round DD at 18.75 kHz instead of the elliptical that comes in the Gold Pack. I think some dealers refer to that as the Relic pack. It would still be a good idea to silicon it as described above as it too is considered water resistant. Then, depending on your soil conditions, you might want to add either the small DD or the small concentric for better target separation in trashy areas. JMHO HH Randy