Generally films touch me more, but that's purely because a) there are more films to choose from and b) there are huge segments of entertainment that aren't trying to touch you, and gaming tends to fall into that. Speaking broadly, the vast majority of action movies and horror movies aren't trying to touch you emotionally, or aren't going to succeed at it, and that's fine. Likewise, a lot of action games aren't going to try to make you cry, and they don't have to make you cry to be good.
However, while I may have been touched by more films than games, I will say that individual games which touch me probably do so more than the individual films which touch me. Games which are able to reach me emotionally are able to do so way more often, both because of how much longer games are than films, but also because games have the added advantage of letting you shape your own experience.
Moments that get to you don't have to be something some writer artificially constructed and scripted, or a director chose to make you feel a certain way. I've had touching moments in games that have been entirely of my own creation, in free-roaming games like Fallout 3. All of the most emotionally significant moments I had in Fallout 3 were ones that came about purely because of how I roleplayed that game, and how I chose to view the Wanderer as a character, and make all their actions, including mistakes, inform that character. It made for a far more enriching experience.
A player character that I initially thought of as a blank slate and couldn't have cared less about when the game first started wound up, through my actions, becoming this fully realised, 3-dimensional person entirely by accident, with a psychology and motivations that I grew to completely understand. None of it was informed by the game telling me about my character, but by the things the Wanderer could do, and the dialogue they were given. I will probably never be able to replicate my experience with that playthrough of Fallout 3 ever again, but it still provided one of the most fulfilling relationships to a character I have ever had in a game, and totally reinvigorated my passion for role-playing characters in a game.
Excuse that little tangent there, but I think it just goes to show that games have the benefit of a player getting out what they put into it because of the interactivity, whereas films are a lot more on a level of "this touching moment either works or it doesn't work".