In the films droids are largely disregarded as being "dumb" or inferior in every facet... That's kind of a weird way that Lucas plays on classes by showing R2 and 3PO as such pivotal characters while other characters largely treat them like shite. And not just the baddies either...
-Han largely loathes droids. He talks down to them routinely, especially 3PO (but others as well), and treats them merely as objects.
-Obi-Wan Kenobi has disparaging remarks about Droids in the prequals, implying he too doesn't regard them highly, however he seems to change over time and perhaps wisdom, to appreciate R2 and 3PO.
At the same time though, Luke forms a special bond with droids, and yet at the same time Luke has the apparant ability to revert to treating droids as nothing more than slaves or property... So does his father ironically, who treats EVERYTHING like ****. Weird.
In the films though, the battledroids are definitely inferior product... They're, as Brad pointed out, playing the numbers game. While the Separatists maybe have the ability (and did) muster sentient armies for the war, they would largely keep them out of harm's way or use them for pure planetary defense (IE: Geonosians fight on Geonosis alongside Droid armies, Neimoidians fight on Cato Neimoidia but not elsewhere, etc.). The droids are simply a way for the Seps to increase their armies en masse in short periods of time. You figure the Clones took time, and by taking time they got a better product... They were always outnumbered though, but "quality over quantity", as we like to say around here... Better to have 10 great soldiers than 50 inefficient ones.
If you want to take a real-world look at it, look at the Russians in World War 2 (or the allies in general) compared to the German and Axis forces. This is sort of a crude analogy in a way but it's applicable.
In the war between the Soviets and Germany (to narrow it down), the Germans didn't have the manpower to throw into combat because they were being spread thinly. They had fronts in Italy, North Africa, W. Europe eventually... The Russians had one thing Germany didn't, and that was a large population to throw almost entirely at the German incursion into Russia. They dumped men, women, children... Everyone. They also suffered immense casualty rates as compared to the other allied forces.
Though that's not to say similar situations didn't happen to the other allies... For instance, Germany had superior armor in most every way during the war. The Tiger I tank and Panther were vicious compared to the weaker Sherman tank... The Allies in Western Europe and other theaters dumped LOTS of Shermans at the enemy though, and a common tactic for Allied armored columns was to outflank a single Tiger I. The result was usually the loss of 2 or maybe 3 Shermans to that one Tiger, but taking out that one Tiger was a huge loss to the German war machine that was stretched to its limit.
The droids are kind of a similar tactic... Using quantity over quality and gambling that it's what will win the day for you. Sometimes it does, sometimes not.
Come the time of the Galactic Civil War though, I agree with Brad completely that a main reason to not use BD's is simply the fact you outnumber your enemy in numbers and (in theory) superior weapons (be they trained men, blasters, armor, air(space)craft, etc.). The Empire was the dominant force in every way... supposedly.
The Empire (according to EU) dabbles in droid military... They don't abandon it. In EU they use "Tank Droids" extensively for patrol, perimeter defense, crowd supression, etc... They'd be ideal on inhospitable worlds where patrols and things become burdensome (is that a word?) on the stationed troops... Especially if patrols are extended ones. So imagine say a garrison is set up on Tatooine on the fringe of Mos Eisley or Espa... The droid tank could be set to patrol part of the dune sea perhaps, or whatnot. Saves the men who can patrol the city and just on its outskirts perhaps.
Also the Dark Trooper project under General Mohc is an effort to introduce droids into the Imp. Military, however it's an effort to introduce NEW, and vastly superior Droids into the ranks. Droids capable of great destruction and a single unit cable of overwhelming multiple enemies head-on due to its construction (special alloys relatively impervious to damage from blasters, etc.).
The project was perhaps an effort to put sentients out of harm's way (perhaps at the demand of the public who the Emperor would ultimately like to make happy on one level or another). Perhaps it was just a way to get yet another tactical advantage on the growing Alliance, who perhaps were starting to gain an alarming momentum?