After 2000 years, Christian Culture is as diverse as anything that old :)

The 1st one you talked about is a cross. There’re many many different styles of cross:
e.g. Jerusalem, Crusaders', Byzantine, Greek, Celtic, St Peter’s, St Andrew’s ... Every style has its history and cultural background.

The 2nd one you talked about is a crucifix. It is primarily used among Roman Catholic, Eastern Orthodox , certain Lutheran, and Anglican Christians, and emphasizes Christ's sacrifice—his death by crucifixion. I would not suggest you get one if you don’t belong to these denominations.

Symbols are parts of who we are. (is that from Da Vinci Code?:))

My advice to you:
1.Find out which style your denomination uses.
2.Decide one depends on your taste. Then find out the background on the style. It’s will be a great lesson on Church His-story.