I am mostly a prosecutor, but have done some patent litigation as well, so I will chime in on this.
Broadly, patent litigation and patent prosecution practice can be distinguished rather simply. Patent prosecuters generally represent clients up to and including the grant of a patent. Patent litigators generally represent clients after the grant of a patent.
Patent litigation generally involves the representation of clients who are suing another party for patent infringement, or who are being sued by another party for patent infringement. In many ways, a patent litigator's job duties are fundamentally the same as a lawyer practicing any other type of litigation. E.g., patent litigators draft briefs, motions, conduct discovery, etc., just like any other litigating attorney. Indeed, the only real difference between a generic litigator and a patent litigator is the appellate court process (which is not actually that much different), the technical subject matter of the suit, and the relatively small niche of law involved (at least with respect to the pure IP claims in the litigation)
Patent prosecutors generally deal more closely with inventors, and assist in the patent procurement process. This would involve eveerything from taking down patent disclosures, drafting applications, writing responses to office actions, and developing patent strategies for clients. I am finding as I get more experienced that there is also an increasing amount of portfolio development/management involved. The patent prosecutor also engages in a significant amount of client counseling, especially as they become more experienced and deal with clients on a broader basis.
As for the amount of hours and pay, it is generally true that litigators work more hours, and that their schedule is more erratic. Simply put, there are forces outside the litigators control that determine when particular action items are due, and those deadlines can be extremely short. In contrast, a patent prosecutor is having a very bad day if they are suprised by anything on their docket. To put things in perspective, a patent litigator might work three straight weeks without a day off to meet a deadline, and then take a week off after the deadline is met if their case is not moving much. In contrast, patent prosecutors generally work a more consistent schedule. I can say from first hand experience that patent prosecution is not a 9-5 job, so do not get tricked into thinking that it is.
"And am I right that having passed the patent bar will mean nothing if I end up going into IP litigation"
It is not necessary to pass the patent bar to practice IP litigation. However, most practitioners will tell you that having some prosecution experience will make you a better litigator, and vice versa. In my firm, all attorneys are expected to pass the exam. Not to mention that you cannot technically call yourself a patent attorney without having passed the patent bar exam.
" have a follow-up question along the same lines. If one is interested in prosecution and not litigation, is there a reason to go to law school other than the increased salary that one makes as an lawyer as opposed to an agent?"
In a word, yes. As a patent agent, the scope of the work you can do is very limited, relative to a patent attorney. I.e., a patent agent can counsel a client on how the patent process works in the U.S., but could not provide substantive legal advice regarding licensing agreements, patent strategy, freedom to operate, or invalidity.