Well if we are waving the e-peen. I have played everything with the name Final Fantasy slapped on it and every version, port, or remake available in NA since I was young and each main title at least five times (well, except 13). Also including FFXI almost every day from 2003 to 2010 and FFXIV from 1.xx alpha to now. Dragon Quest I have all versions from 1 to 9 you can get in NA including the JP copy of DQ5 and 6 for the Super Famicom and the Monster spin off series. Its nothing major to show off, since most fans of both have likely played them all. Saying I lack knowledge of the history of the series is not a thing however.
Final Fantasy was influenced by Dragon Quest and other games: "At approximately the same time, Square designer Hironobu Sakaguchi began working on an ambitious new fantasy role playing game for the cartridge-based Famicom, inspired in part by Enix's popular Dragon Quest (originally known in the United States as Dragon Warrior)." You can find this mentioned by Sakaguchi himself in most interviews with him about the initial concept of FF. (Also, you got to be pretty damned dense to not see how similar DQ and FF are in design of it's mechanics.)
Source: http://finalfantasy.wikia.com/wiki/F...y_%28Series%29
FFXI was influenced by Everquest: "Final Fantasy XI, Square Enix's other Final Fantasy MMO, was developed as a game where Final Fantasy would meet EverQuest—the top MMORPG of the day. In fact, according to Yoshida, the entire staff played EverQuest for at least a year while developing FFXI, trying to figure out just what exactly made it work so well. "I think it would've been good to do the same thing [for the original FFXIV].""
Source: http://kotaku.com/5963155/new-final-...h-the-original
Ohh look, only took me 5 minutes to find both.