The overall difference is this:
Mangos works to make a stable server where code is optimized, safe, secure and works correctly. No hack code, no workaround, nothing like that.
Trinity works to have everything that wow has to offer, that includes vehicles, battlegrounds, etc... but at the expense of having a whole bunch of workarounds, hackish code, etc.. which leads to unstable version.
the easiest way to check this out is, read the commits for mangos for the last 100 entries. Then read the last 100 for trinity. Tell me in which you find commits like "Corrected a crash for X problem" or "Correct typo for memory problem". Since they use a lot of hack code and workaround the get more stability issues. For myself i used trinity for 2 days and had about 15 to 20 crashes. I used mangos for 9 days straight. No crash whatsoever. See my point. You can either go for stability or the other one. Which does not mean that both are working to achieve a more stable, complete version of themselves.