A good old fashioned Doctor Who Community
What are some of your past favorite Tennant episodes or moments? 
"The Satan Pit" and the second part "The Impossible Planet" are among my favorites. (The stuff of legend).
I also liked "Journey's End". He burned a up a sun just to say goodbye to Rose, a truly heartbreaking moment.
10 and 11 are pretty much tied for my favorite iterations, both special in their own ways. One of my favorite things about 10 was his care for "little" things while dealing with universe threatening events. From little shops in hospitals, to old men trapped in a box. The other generations cared about those things in their way too, sure, but he cared about them just as much as the biggest of things he had or would face. And not in a quippy way, where it could be played off as a gag, but genuine care. His run was just great.
*Another characteristic of 10 that I love - his core need/desire to give every foe he faces a chance, at times pleading with them to stop or change, not because he couldn't stop them, but because he genuinely would rather be friends with them, and would spare them the misery of dealing with what he ends up doing to stop them otherwise.
old men trapped in a box
If this is referring to "Four Knocks" from the "End of Time Pt2" with Wilfred, this was a very heartfelt moment.
His ranting about how he could be so much more, really pulled at the heart strings. He knew his end was inevitable even though he had fought it for so long. Telling Wilfred "It would be my honor", after his rant was an emotional slingshot.
I thought Tennant had a way of being very realistically emotional, a trait not usually portrayed by older generations.
Another characteristic of 10 that I love - his core need/desire to give every foe he faces a chance
In "School Reunion", he comments how he used to have so much mercy, and implies since he is older now there is not much mercy left to give.
From 10's first episode he said "No second chances. I'm that sort of a man".
While he is still willing to give mercy, at this point in the Doctor's timeline I thinkTennant does a decent job in portraying how weary he has become.