I see five primary differences.
1) Court Filings And Data Are Usually Public
Much of litigator's final work, if not actually out in the open, is publicly accessible. That means that it is possible to cross-check or pull in relevant, helpful documents from outside the firm (the other side's position might well be yours in the next case).
It also means that effort spent on tracking some types of information, like who in your firm has appeared before a particular federal judge, can better be spent elsewhere as it may be available through services like Lexis' Courtlink.
Down the road, as I have commented earlier, there is great (as-yet unrealized) potential for caselaw search based on free public access to court opinions.
2) Calendaring / Docketing Really Matters
Calendaring is much more important for litigators than for people who make deals. We even have a special name for it--"docketing", which technically refers to either filing of a pleading or motion in court or the entry of a deadline for the same type of activity (or a discovery deadline) on an internal calendar. Some large law firms even have centralized "Docketing Departments."
Obviously there are deal deadlines, but there are so many more deadlines in court, and missing them can be so harmful, that deadline tracking systems, technological and otherwise, are of critical importance.
3) Practice Areas Don't Matter (as much)
My firm is organized (in descending level of order) around Departments (two), Major Practice Groups, and Practice Areas (~35--the smallest unit). While different practice areas on the business side of the firm have quite different knowledge management needs, litigation groups have largely compatible knowledge management needs.
For instance, litigators want to be able to find all firm work product that cites to a particular case or statute (thank you, West KM!). They need to track ongoing trials as a group, and so on and so forth.
Practice-area specific KM is certainly viable in litigation, but many of the most effective KM efforts benefit the entire litigation department rather than a particular litigation practice area.
4) DMS Use Differs
Document management system use is also slightly different. While litigators negotiate documents outside the firewall, it is not the main thrust of our efforts. Therefore, versioning, redlining, and importing files from outside as new versions of DMS documents all tend to be less important than they are on the corporate and real estate sides of the firm. Final versions of documents are available from courts and pleadings systems, as well as from the DMS. Another DMS difference I've developed at Goodwin is pulling in "forum" matters data directly into the DMS for use by our litigators. I'm not aware of any comparable business-department-wide piece of matters data.
5) Bleak House vs. Let's Make A Deal
Litigation cases on average take much longer than deals. With the amount of work being relatively equal, that means that A) there are proportionally fewer litigation matters than deal matters and B) different time horizons have to be considered for all kinds of support systems.
There may also be some difference with respect to reliance on case law, though I am less certain of that proposition. It may be that business lawyers rely on cases as much, but simply don't like to use Bluebook form in their cites).
The above are my opinions as a litigation KM practitioner. These general distinctions tend to blur in the context of high-volume, commoditized litigation, and where deals blend into dispute resolution and administrative agency work.