Height and width both have advantages and disadvantages. All of this has been covered pretty definitively here and elsewhere, but here's the cliffsnotes version.
+Height = increases ground clearance. No substitute.
+Width = increases contact patch. [Lateral stability, tread contact (traction)]
The extent of these advantages is only as good as the terrain you use them on. The trick is understanding the limits. Narrow tires "dig" and wider tires "float". Making wide tires better for "deep" terrain (dunes, beaches, swamps, mud holes, loose river bottoms) and narrow tires arguably better in hard pack and "shallower" conditions where you want to cut into or through the terrain for maneuverability (moderate snow, water crossings, and generally sloppy weather).
A narrow tire should weigh less, but lack stability in off kilter scenarios due to sidewall deflection. A wider tire will add stability on rocks, but add scrub and track width which can make navigating tight forest trails strenuous.
Examine the terrain you regularly encounter and weigh that against the cost and effort of the modification required. No one rig will be able to tackle every terrain. It's about arming yourself with the best strategy. Allowing all of your parts to complement each other in the area it's best suited.
TL;DR:
Yes you can keep your tire size and be fine on lots of terrain. You can run tall narrow tires and keep up with most of your friends. That is, until you reach the limits of the size you choose.
Hope some of this helps. There's a lot of info to find on tire sizes and styles. I recommend devoting a week to researching opinions and combinations as well as pricing. It will definitely pay off.
Cheers
