[finnster]

I agree and disagree with some of the points made about the two guitars from the OP.

Agree:
-I would not consider either the LX1E or LX1E Ed Sheeran as good mid-range guitars. They are very small travel guitars with durable high pressure laminate construction. Given this, they are the kind of guitar that packs easily, can withstand climate changes and at the same time offers decent (certainly not great) tone. I have played both and own the Ed Sheeran model - IMHO the Sheeran model sounds better than the other Little Martins (owing to the nice solid Sapele top).
-I agree that the GS Mini sounds much better than any of the Little Martins (I owned a GS Mini previously). However I wouldn't even try and compare the two. The Little Martins have an edge in durability and ruggedness and that's why I got one.

Disagree:
-IMO the Little Martins are not terrible - they are decent little guitars for traveling with, taking camping, taking to work (I do this with mine all the time) and not having to worry much about damage, etc. Yes they sound boxy, I think any guitar this small would. For me they serve a purpose that I wouldn't want to subject other guitars too, and keeps a guitar in my hands when I might otherwise not have one. YMMV.

To the OP, if you are looking for a good mid-range everyday player and do not have the specific size and durability requirements of a Little Martin - I would look at other options. There are tons of other better choices.