In US use (in my experience) both have negative connotations. The word "mean" is far more often used in the sense of "cruel" or "nasty", and so when it is used to mean "unwilling to spend money" it picks up some of the negative attitude from that more common use. That would not affect "tight" so much, but the related from "tightfisted" is more negative. "Tight with a dollar" can be quite negative, or not, depending on tone of voice and context.
As a comment points out "cheap" can also be used for this meaning. It is negative, but usually not as negative as "mean" or "tightfisted". Of course context and tone can make a significant difference in the meaning.
If, in US use, one wants to indicate that a person does not like to spend money, without being negative, perhaps even while being friendly, one might say that the person is "frugal" or "thrifty" or "not extravagant". The latter is an example of ironic understatement.