Pros
If you find a position right for you on a team that is in one of IBM's core businesses, you'll probably be happy. There are lots of good people in "Big Blue," some of which are extremely well connected in global terms, opening doors to potential opportunities. Strong work and leadership are likely to be recognized and leveraged and, in time, rewarded. Size and stability can raise security, which is especially useful for people with families or other long term responsibilities. There are a broad range of businesses and roles, lateral moves into areas of preference or growth are quite possible.
Cons
The company is a behemoth, and with large scale comes processes and cold impersonality - its unavoidable. The company had laudable policies re "people first" and compensation, much of that has gone away. If you're outside the mainstream business, you'll likely be struggling for resources and the attention of policy makers. Much of the internal technology si not competitive with what we find on the internet, and this is an unfortunate burden for the company. Opportunities are subject to the usual competition, do not go to IBM expecting to be a software architect without proving yourself for a decade or more of dues against a bunch of talented others.