As one of FIVE children in my family to go through Dickinson Elementary from 1993 - 2007, I feel I can adequately comment on this subject.
Dickinson and Campbell both pull exclusively from the Greatwood subdivision and serve grades Kindergarten thru 5th grade.
Lamar Consolidated Independent School District - District Map
Lamar Consolidated Independent School District - School Listing
They are both part of the growing Lamar Consolidated School district and funnel into the George Ranch campuses (Reading for 6th - 8th (until the 6th grade campus is built, then that will be a standalone campus while Reading Jr High will have solely 7th and 8th graders) and George Ranch HS for 9th thru 12th). LCISD gets a bad rap from people who don't know any better - they think of LCISD as a behind the times, slightly ghetto, blue collar & farm school district. While various high schools pull from a range of socio-economic areas, academically they are outstanding and provide unique opportunities for those that attend. The fight to be in the top 10% of your graduating high school class (for college admission purposes) is somewhat easier in LCISD without sacrificing the overall quality of the students' education. Also, LCISD is committed to keeping its high schools in 4A (roughly 1500 - 2000 student enrollment), which provide opportunities in athletics that may not otherwise be as accessible in their 5A FBISD counterparts. In addition, George Ranch is probably best or a close 2nd academically behind Foster (this is coming from a Lamar HS grad, mind you) and less "ghetto", if you buy into that sort of thing.
Both schools are recognized/exemplary elementary schools (depending upon the year and their respective test scores).
Both schools have the same dress code (simple uniforms - polo shirts and slacks, and I believe maybe a few "casual" days where they can wear jeans and their respective school's t-shirts, though I imagine this may have expanded since my days there).
Both schools have amazing teachers, many of whom have been in the district for years (several teachers that were teaching while I attended through 2000 are still there), so I figure they must enjoy and care about their jobs and the students.
There are a few marginal differences between the two that may be factual or purely based on perception, but from what I have observed (having lived in both the "front" (read: "old") of Greatwood and "back" (read: "new") of Greatwood), those differences probably have more to do with the parents and their age than the administrations themselves.
I feel that both schools go to great lengths to support both the arts and physical activity with their staff and programs, and make it a point to be very involved in the community and finding ways for the community to be involved in the school.
Discipline - I don't have much experience on this, as the only time I spent in the principle's office was when my bike was stolen in 4th grade because I didn't have the sense to utilize a bike lock. As far as I recall it's the pretty standard "change your color / flip your card / move your clothespin from green - yellow - orange - red" in-classroom discipline process, with orange sending a note home to the parent and red a visit to the principle (rarely). I mean, they aren't using the paddle or anything.
What you have most likely perceived from the schools' newsletters is true - these two schools care about the well-being and development of your children.