Old thread, but here are my $0.02:
I would say that it depended a lot on exactly what software and what hardware it was.
I.E. for example if the target was a Commodore 64 then any search operations on larger databases would have to run in the disk drive as it would read disks about as fast as a PC or any other computer with 5.25" DD drives, while data transfers between the drive and computer were painfully slow.
Also at least before PCs more or less no microcomputer had enough RAM to keep all data in RAM if we for example talk about book keeping for a small mon-and-pop style shop company.
Those companies would typically have one voucher (??? Swedish "verifikation) per business day, and a few extras for special things. Like one voucher with the data from the cash register, that might have had say 10-20 stock categories that all items were lumped in under. So for example a grocery store would probably have had book keeping and cash register categories for vegetables, meat products, diary products, bread and such, but no way of distinguishing beef from ham, milk from cream or lettuce from tomatoes. Same for a consumer electronics store, "hifi", "portabel audio", "TVs", "VCRs", "accessories" and such would the categories probably be. Thus each daily voucher would contain a line for each of these categories, and then a line for each payment method, and a line for VAT. (Multiple lines for shops that had different VAT levels ; here in Sweden for example grocery stores have every now and then had had lower VAT for food than for other products).
I don't know if book keeping software used "double-entry bookkeeping" within the software, or if they just stored one of the two ways of representing the data and generated the other when viewing data.
Anyways, the amount of data at the time for that type of shop was at the time slightly too much for the available book keeping software for a C64 to handle (V-Bok from ADB-Väst here in Sweden), while software that would comfortably run on a PC/XT and where the data files would fit on a 360k disk would have enough capacity. This is IMHO really interesting since a C64 1541 disk had a 170k capacity, I.E. slightly below half of a PC 360k disk. I don't know if the C128+1571 version of that book keeping software would be enough for that type of business.
Btw, Apple II weren't common here in Sweden, but this makes me wonder to what extent Apple II were used for book keeping? As I understand it on one hand it was more common to have two drives than say with a C64, but on the other hand the capacity of each disk were even lower (early on 113k, later 140k, as compared to Commodores 170k).
Other small businesses that didn't have a shop where customers walked in could easily use those less capable book keeping packages though. I.E. say a farm, a contractor running heavy machinery or whatnot, that would just have a few vouchers each month, would have way less data than a C64 could handle.
Also re speed: Note that speed had to be compared to doing things manually. And also, for book keeping I think that searches weren't done that often. I.E. you entered things in order to comply with regulations. Today you probably combine book keeping with a more fine grained inventory system, and actually use it all as data for how your business performs. Back in the days book keeping was a necessary must that the book keeping department at larger companies, or for a smaller company a secretary, the owner themselves or a book keeping company would do, and the data was just used to file in tax reports and whatnot. There for sure must had been companies that had more modern style systems, like how I think people talking about AS/400 / IBM i mentions that Target still uses IBM i and probably used it back in the days. But that would probably be more of an exception than the rule.
Also: business software were really expensive! I haven't dug that deep but a quick google AI summary states that Hogia, the most well known microcomputer book keeping software here in Sweden, cost between a few thousand to ten thousand SEK, which you can roughly convert to EUR by dividing by ten. But that was in 1980's money, so would be the equivalent of way more in today's money value.
A related story: A company called Swedish Partner made a file compatible program called Masterbok, which they sold way cheaper. It was said that it was just a rewrite in another language, and in particular that software came with files with names like "BRUN.EXE" and whatnot, which makes me think that it was written in Basic. A the time it seems like a common setup would be that a book keeping company would run the expensive Hogia software while clients would run Masterbok, and the clients would enter their vouchers and whatnot and once a year send/give a disk to the accountant company which would then do the end-of-year thing, calculating/filing taxes and whatnot, which was the part of book keeping where you needed to keep up to date with regulations. (Like I remember a bit from book keeping back in the 1980's and when seeing the book keeping from a NGO I was part of in the early 2010's the only major change was that the account number for cash was moved from 1010 to IIRC somewhere in the 17xx or 19xx range. In other words there were like one change in 20-30 years that you had to know if you just entered the vouchers, and that was also a change that would only happen when starting a company (or NGO or whatnot). I think that you wouldn't change account numbers for the book keeping of an existing company unless something really extraordinary would happen.
Re inventory:
I've always wondered what companies actually used inventory systems, except for super large companies that could go for IBM mainframe stuff?
Say if you run some sort of mechanics shop - the inventory would be useless unless it kept track of each type of bolt, nut and washer. The same goes for say repairing consumer electronics - you couldn't use an inventory system to automatically restock unless it kept track of every single component. And every such shop would have all standard E12 resistor values in the 10 ohms to 10 megaohm range, for a few different max power ratings. The resistors alone would he 721 values for each power rating. If you had 1/4W, ½W, 1W and 2W that would be 2884 different items. And then you'd have to key in what was consumed when doing repairs. The other option would be to just look in your drawers and order the items that you ran low on.
A somewhat related tangent: There were also sellers focusing on charging for the comfort of not having to keep track of your stock. Here in Sweden one of those were Moon Radio, where their seller would visit you and check your component inventory and suggest what you'd order, and then you'd end up paying perhaps 5x the cost of buying from general components importers (where you had to phone/mail/fax in your order yourself).
Also the consumption rate was low. Like say if you spent an hour repairing a TV you might end up having replaced a few resistors, a transistor or two, and perhaps a few capacitors or so. Or in some cases replace one or in rare cases two IC's. Thus there weren't that much demand for restocking components.
Another tangent: For some businesses the accounting and inventory system would probably still struggle for being the main source of data. I.E. for a grocery store you'd also need the expiration date for items, otherwise you'd have to manually enter what items you'd first sell at reduced rate and later have to throw away (I bet that in practice those items ends up as untaxed employee benefits...).
Also: In addition to book keeping, I bet that word processing was the by far mostly used software for small companies. You could just have a template where you'd manually enter the customer name and items for sending invoices, without having any mail merge or inventory/order system connected to it, and still save lots of work while also making it look "professional". Yes, beleive it or not, some customers would treat invoices as more "serious" if they were printed using a dot matrix printer than if they were hand written or written using a typewriter (or for that sake a LQ printer). A smaller company would never for example order paper with pre printed letter headers and whatnot, and thus having that already in place for in invoice would be a great time saving as compared to writing it using a type writer. (They would likely have a pre made stamp with the company name, address and phone number(s) though, so for hand written invoices you'd just put that stamp on the invoice rather than typing that all out).
Edit: In case anyone is intereted, I have a copy of Masterbok but it has the customer name in the executables. That customer doesn't exist but public records and whatnot would dox where I got it, so I can't really share it (could put it on some sort of to-share whenever I'm not with us any more though, if that's even possible). I could check which files are part of it, and if anyone is interested I could also run experiments / analyze it. I.E. send me some software that checks for "signatures" for what it was written in and whatnot and I could try that out (on a virtualized/emulated machine).