I don´t know STW, so I can only compare RTW and MTW, but, anyways, here goes:
The most important thing (the battles, hey, the name of the game is "Total War", so it´s all about that) are fairly similar, yet there are differences. Apart from the graphics, the RTW control is - in my opinion - somewhat more "foolproof" with the left-click select/right-click move setting, but somehow it makes for a bit harder controls, when it comes to unit facing and rank selection. On the other hand, you can arrange your units in RTW in the beginning of each battle, be it defensive or offensive. In MTW you can place the individual units only in sieges and defense battles, when attacking you have to stick to a selection of template formations. RTW battles move a lot faster (or so it seems to me), MTW leaves a bit more time for thinking - which is direly needed, terrain and Generals make huge impacts and mistakes are punished severly.
Sieges are not that much different, in RTW you have more siege equipment (like rams, siege towers, ladders and tunnels) than in MTW, where artillery is the only heavy equipment ever used.

As already mentioned, the biggest difference is the strategy map, in MTW it´s a bit like the board game "Risk", while in RTW you can move your units to any place - which can be used to gain advantages on the battle map, be it by blocking a bridge or maneuvering reinforcements into your enemy´s back. RTW also has more diplomatic options, in MTW you can be allied, neutral or at war, in RTW you can secure trade rights, become Protector of a faction, buy and sell map information, instingate attacks on third parties etc. RTW, however, lacks the religious aspect of MTW, unless you´ve got the Barbarian Invasion expansion.

I can´t really recommend one over the other, personally, I´ve started with RTW, but I´ve grown to appreciate MTW a lot, too.