Bluesky, I've had the pleasure of working with the people of both cities. Of course they've probably both got their good and bad points.
Manchester has a more "cosmopolitan" feel to it, and has developed considerably over the past 10yrs. I'd suggest Liverpool is probably more culturally diverse, and, as an ancient port, more historic.
Geographically, Liverpool is closer to "the coast" and offers easy access to North Wales, Lynn Peninnsula and Snowdonia. Manchester offers easy access to the Peak District, Lake District and the North Yorkshire Moors.
As with most inner cities, they both have problems with crime and anti-social behviour. Manchester Council is probably more rigorous at dealing with this problem. Acual crime rates are pretty simillar, although perceptions towards Liverpool people are often worse, as demonstrated on this forum. The direct approach of "scousers" doesn't always suit everybodies sensibilities!
As to the acts of vandalism (eg the gravestone issue), unfortunately this happens in both cities. You will find that rates of crime, quality of schools, rubbish on the street etc is directly related to the price you pay for your property.
On a one to one level, people tend to be friendly and accommodating in both cities.
City living isn't for me, I choose to live in the "Green belt" as described earlier in this forum. I have friends who regularly visit both towns, and enjoy the diversity they offer.
Cheers.