One of the major developments with Eagle 7.1 was the multi core auto routing engine, I don't often auto but it did seem to shimmy along when running a test case.
I have never had Eagle crash on me, I've asked it to do a lot of crap over the years, and it has been absolutely fine.
In terms of DT vs Eagle, well, that's a whole other can of worms you have opened up!
I use Altium and Eagle, almost daily, but have used other packages, I used to use Proteus in a previous life, I have tried DT, AutoTrax, I downloaded, and then removed it, it felt too heavy for me, massive tool bars etc, but that's not to say it isn't good, but read the forums, the owner is very arrogant, but apparently is quick to fix bugs.
I never got on with DT, but again, it is a good package, the only thing that seems to be missing feature wise over Eagle is high speed design, if you are not interested in differential pairs or length matching (though I've heard that is on their hit list of new features) then there is no reason not to try it, Proteus is an expensive package for example, and doesn't have high speed tools, bang for buck Eagle isn't bad, DT is even cheaper still, and it can import Eagle files I believe, it has native 3D rendering (useful for case fitments etc), I am used to Eagle so I am reluctant to move as it does everything I need it to do.
Something else that has come on a long way is KiCAD, free, open source, more frustrating to learn than Eagle, but you are free to use it as you wish.