I have never taken Eltroxin (it isn't available in the US, officially), but can offer this insight:
All Synthetic thyroid meds (Eltroxin, Levothroid, Levoxyl, Levo-T, Synthroid, Unithroid, etc.) contain the same active ingredient, Levothyroxine Sodium.
The difference between the brands is in the fillers that are used to give the pills their shape, size, color, and texture. The differences in fillers can affect the way you absorb the active part of the pills. One person may absorb Synthroid better than Eltroxin, but the next person may absorb the Eltroxin better.
The best advice I can offer you is that if you DO switch brands, then get labs done 6-8 weeks after the switch and adjust your dose if necessary at that time.
I am not a doctor, nor have I ever played one on TV...
I started out on eltroxin when I was 9, but quit taking it when I was 16 because of the side affects. (I felt depressed when I took them, was fine when I was on nothing). I started three different trials of synthroid when I was 19 till last October (now 21) and the only differnce I felt was they made me more anxious, even though I was on a very low dosage. But my experience is weird, let me know if you have any changes!