I know you said you don't game on PC, but I recommend to at least check this site, where you can find some of the PC games recommended in this thread: http://www.gog.com/en/catalogue#strategy/ (the list includes TBS, RTS and bulding/economic sims like The Settlers, Patrician or Port Royale - as for some reason most websites these days file all building/economic sims except SimCity under strategy games).
Most of these games will run on any modern PC. Heroes of Might & Magic III, Age of Wonders games, Disciples 2 are some of my favourites from this list which still look good today imo, but I liked Master of Magic, Master of Orion and Jagged Alliance even more.
The list is missing the imo best TBS series (and one of the best gaming franchises) ever created:
Civilization. You already played the very good, streamlined console/handheld port CivRev, but nothing comes close to the original series (my fav will always be Civ 1, but objectively Civ 2 and 4 are the best).
I've never played a game from the popular Worms franchise (TBS subgenre artillery games), but this might also be something for you and a Worms game is available on every system, i.e. also on XBL.
On handheld/console I'd generally recommend SRPGs instead:
Fire Emblem (DS), Final Fantasy Tactics (DS, PSP), Valkyria Chronicles (PS3, PSP), Jeanne D'Arc (PSP), Disgaea (DS/PSP/PS3), Luminous Arc (DS),...
Fact: The best TBS franchise not on PC is Advance Wars (DS).
And here's a special tip as you liked CivRev:
I'm not sure if you have a DS, but Age of Empires - the most famous PC RTS franchise - is surprisingly a TBS franchise on DS. Both AoE games on DS (The Age of Kings, Mythologies) are great and should be very cheap today.