Part of my block army collection includes units for fighting actions set during WW2. In the games folder there is a number of games I fought ranging from the pine forests of the Eastern Front via France and Belgium during 1944 and the Greek Islands in 1943. They were all good fun to fight and I used a combination of both a hexagonal and a square grid.
The only hexagonal playing surfaces I now own are the laminated and geomorphic maps that originally came with the Axis and Allies WW2 collectable miniatures game and these have seen much service with the block armies. Unfortunately, as far as I know, they never produced a desert map which is a shame. There is of course the old standby of the Memoir '44 map boards but these are a little on the small side for the blocks - as are the Heroscape tiles I still have unless I use a single block units.
Bob Cordery has, through the medium of his Portable Wargame series of books, outlined the advantages and disadvantages of squared, hexed and offset squared grids which was very useful. For my own part I am leaning more and more towards using a square grid for those games where I need to use one. The biggest hurdle in using a square grid has always been the old chestnut of allowing for diagonal movement and firing. There are ways to allay this and I have previously mentioned the system adopted in the Napoleonic naval rules 'Ship 'O the Line' originally published in the early 1970s (and the forerunner of the excellent Avalon Hill board game Wooden Ships and Iron Men - ironically using a hex grid rather than the square version of the original rules) which adjusts diagonal distances to match as closely as possible to the orthogonal versions.
Within the Portable Wargame I simply allow a unit to make a single diagonal move during its movement as the rates are quite low so the distortion is minimal. This has the effect of really opening up the board especially if you also extend the same to direct fire. Essentially you can work with 8 possible directions of movement or firing rather than the 6 of a hex. I would also argue that it is easier making terrain to fit in a square rather than a hex!
Using a square for naval games has the advantage of being able to reference natural compass headings and again, with 8 directions available rather than 6. As movement is an important consideration for naval gamers again you can see the practical advantage of using squares.
Taking the above into consideration I have decided that my games will primarily be fought on a square grid. Using the diagonal option from the naval rules mentioned as a guide means that a square grid is far more open and, dare I say it, natural in respect of facings etc.
When I decided to include WW2 in the great block project I was really torn as to how best to represent vehicles. Tanks, SP Guns, Armoured Cars, Trucks, Half Tracks and all the permutations associated with them really gave me some problems as I was unsure whether to draw representational types or to go down the military map symbol route. After much thought I decided to go down the military symbol route and opted to use combinations of blocks to represent specific types. For example, an armoured infantry unit would consist of three infantry blocks and an armour block. You can see what I mean looking at the game above.