The latest "Total War" series go to great pains to reflect the geography / military situation you see on the main map, with the type of battle that you then fight on the battle map, (i.e if there is a river on the left and enemy stacks North and South, then that's the actual battle you fight. The battles can involve several thousand units, if there are multiple stacks and the battle maps contain an extraordinary amount of detail, and more than you have asked for.....
But.........
"TW" just does not have the huge replaying power of Civ.
"TW" is well worth playing, but there are weaknesses to it's re playability:
1) The main continent map is always the same, the civs and resources always start in the same places, and there just isn't that feeling of discovery you get in the early part of Civ. Each Civ game is truly unique and every start is utterly random and unknown. TW has a completely predictable start, once you have played it a few times.
2) The TW "battle maps" are a huge amount of fun, and you can create a very unique army with different strengths and weaknesses, and every unit can gain veterancy or be upgraded by tech, but you have to fight a HUGE number of battles, Yes, you can risk the "auto resolve" button when faced with a simple battle you should win easily, but the human player can do a much, much better job than the computer, and you therefore have to fight every battle yourself, just to keep hold of your veteran troops and generals. As much fun as the battles are, the sheer number of battles you have to fight just becomes very frustrating after a while. If you think about how many battles there are to fight in some "civ" games the problem would become infinitely worse, if there was a "battle map" in Civ. If games developers could design an "auto resolve" that produced a result that was vaguely fair, then we would only have to fight the really important battles ourselves, (rather than every single one of them), but this tends to defeat the whole point of having a "battle map".
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The "TW" series is soon to release their latest game in the series, and it will be set during the age of discovery, and many fans hope it will be an evolution on "TW2" which many people were mildly disappointed by. The previous version "TW:Rome" felt like a genuine evolution of the game series, whereas "Med2" just felt like Rome with a few new skins and fancier graphics.
So, the "TW" series does everything the OP asked for, and more, and it is great fun, but it just does not have the re playability of the Civ series, (yet?).
On balance I would therefore prefer it if Civ5 did NOT have a "battle map" as it just doesn't work yet.
I'm looking forward to the new "TW" game, (this Summer?), as it it will be the first game in the series to feature naval battle maps, and that should be extra fun. For me, the "Test of Time" (excuse the pun), of the new "TW" game will be how long it takes before I am forced to fight a battle on the "battle map" that I can't really be arsed to fight, because I am clearly going to win it, but if I hit auto resolve I risk an uncertain outcome and the loss of an unacceptable number of key troops / generals, so I have to fight it = groan.
Regards - Mr P