I think the general goals for an E6 project are twofold.
1) Limit magic commonly accessible to the PCs to 3rd level (with the possibility of very limited access to 4th+ spells). Higher level magic is limited to the DM, and generally the realm of powerful monsters and legends.
2) PCs at the peak of progression should still be mortal heroes. A max-level warrior might be able to fend off 5-6 guards, but a dozen crossbowmen is going to be a fatal encounter.
I think for item 2, we need to ascertain a benchmark for what makes a mortal hero. 3e used 6th level, of course, but I think we all know 3e scales much faster than 5e with bounded accuracy in place.
Personally, I like about 60 HP for a warrior-type as a good benchmark for a mortal hero. It means a long fall (doing 20d6) is more than likely to kill you. 12 crossbowmen doing 1d10+2 will probably kill you in a round, assuming about a 60-65% hit rate.
So a 5th level warrior would have about 49 HP, normally, assuming 16 Con. 6th level would be 58 HP. So yea, 5th or 6th level both work pretty well; 6th lets you start right around 60, 5th lets you grow into it (assuming increased Con over time and dice shenanigans like the WWN rule.)