If you already play in either Open C (CGCGCE) or Open G (DGDGBD), you can transpose a lot of the chords, whole tunes/accompaniments in fact, from one to the other.
Before I explain how, it's really useful to understand Roman Numeral Notation (RNN).
From the table on that page, we have for the two tunings:
| RNN | C Major | G Major |
|---|---|---|
| I | C Major | G Major |
| ii | D Minor | A Minor |
| iii | E Minor | B Minor |
| IV | F Major | C Major |
| V | G Major | D Major |
| vi | A Minor | E Minor |
To transpose a roman numeral chord from Open G to Open C, move the whole shape up one string, and vice versa.
For example, this shape is a I (G Major) in Open G ...
| D | || | | | | | | | | | | | |||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| B | || | | | | | 1 | | | | | | | ||||
| G | || | | | | | | | | | | | |||||
| D | || | | | | | | | | | | | |||||
| G | || | | | | | | | 2 | | | | | ||||
| D | || | | | | | | | | | 3 | | |
So this shape is a I (C Major) in Open C ...
| E | || | | | | | 1 | | | | | | | ||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| C | || | | | | | | | | | | | |||||
| G | || | | | | | | | | | | | |||||
| C | || | | | | | | | 2 | | | | | ||||
| G | || | | | | | | | | | 3 | | | ||||
| C | || | | | | | | | | | | |
and so on ...
Obviously, you have to do a little more work where the shape has a finger-position that falls off the edge of the fret-board as you transpose, but basically this really useful fact means that if you can already play anything in G in Open G, you can play it almost without new learning in C in Open C, just by moving the whole tune's shapes up one string. Equally, if you already play in Open C, you can play in Open G just by moving shapes down one string.