As you said: two different beasts.
To be honest I've not tested them against each other (I've only got the Magni for a week).
I bought the LD1+ mainly for my Grado's (325is) and it's great for them.
I bought the Magni mainly for my Fischer FA-011 because I was not happy with the sound of them on the LD1+, especially on the low gain setting. I got tired of opening the unit to change the gain setting everytime I wanted to use the FA-011's (especially since it wasn't a great match anyway). The Magni however has made me love the FA-011's as much as I love my Grados with the LD1+.
I dont loke the Grado's on the Magni very much but I've not listned much to this combination yet (to harsh).
I have a set of NE 408a tubes and a 2107 op amp in the LD making it rather warm sounding (great with the Grado's) .
The Magni is more neutral (no surprise there) and also more analytical i comparison. This is what I expected and why I bought it. I think these two amps will take care of my amp needs for a long time (the LD is also very flexible and gives the possibility to play around with op amps and tubes).
So hopefully I will not need to buy another amp in a long time.