I have both, neither one very serious, but they are extremely handy. I use the scope way more than the LA, and the only time it really comes out is when I need to debug a stream of data.
You don't get both with any instrument.
You can, my scope is a Kenwood DSO from 1987, its only 20Mhz, but its a CRT based machine with both analog and digital storage functionality, and its very rare that I switch it over into analog mode. Last time I did I was looking at a 28.something Mhz crystal and the DSO couldnt latch onto the very short peeks 8Mhz past its bandwidth (but the analog function showed it).
Fully digital seems to be king, cause its cheap, and today its pretty damn fast, there is always a hint of lag, but there is so much memory available and features in modern models, it more than makes up for it.