I don't believe the 777-300ER is used for both flights from EWR-TLV. I think it depends on the day. I also think you have a good chance of upgrading. As noted above, there are certain days that are better than others. Shabbat and middle of the week.
Harder on the 777-200, I think because, I believe, there are less seats up front. Plus, the Polaris on that is not Polaris. Same with SFO to TLV.
Also, if you fly SFO to FRA then I think Lufthansa uses the Airbus for FRA-TLV and, if I recall, it is not lie flat. And I think it is about a 4 hour flight. Seems like going through SFO would add a lot of time and much (or all) of that extra time in a non-lie flat.