Totally in agreement with Steve
To add to that: out of the box, SHIII doesn't offer anything that SHIV and SHV don't do as well or better - except for a couple of additional U-boat types and a longer, more comprehensive campaign. Otherwise, IV and V are better than stock SHIII in virtually every way.
However, with modding, that picture changes rather drastically. SHIII has been expanded and added onto so much by mods that it's by far the most fully-featured of the bunch. From improvements to sensors and evasion, to Type XXIIIs, to working wolfpacks and virtually all previously-missing ships, aircraft and weapons, to SHIII commander, it has by far the most complete package and a lot of options to boot.
That said, TMO, RSRD and Op Monsun? Fantastic mods which offer some things which SH3 can't have! Even on the Uboat side, Op Monsun for example has by far the best (most historically accurate) campaign traffic and mission structure.
Like Steve, I wish we could have had more work done on SHIV. But on the bright side, that leaves lots of great things in SHIII that are very worth exploring on their own merits.