To my mind, the most crucial issue is education. Travellers have both practical barriers and negative attitudes towards education, leading to the lowest literacy rates of any demographic in Britain. A majority of traveller children do not complete primary education.
Given the immense importance of education in the modern world, it is inevitable that travellers will be economically and socially marginalised. Illiteracy poses a near-impassible barrier to engagement with mainstream society.
Significant effort has been made in the UK to engage traveller families in education, but to no avail; school attendance and educational attainment is actually declining among traveller children.
Unless this impasse is broken, there is little hope for travellers.
https://ore.exeter.ac.uk/repository/bitstream/handle/10871/1... http://wikireadia.org.uk/index.php?title=Travellers_and_lite... http://sro.sussex.ac.uk/38614/1/McCaffery%2C_Juliet.pdf
You've raised the issue in a well-reasoned manner which largely avoids being gratuitous. Your discomfort at saying this suggests that you would otherwise prefer to view the Roma as decent people, and there is little to make one doubt you'd be happy to afford them the rights and dignities which all of mankind deserve.
Others here have presented the case in far nastier ways and their comments have gotten the predictable flag / kill treatment.
Not to say that elements within either group haven't been responsible for some of the things you mention, or that there aren't any similarities. But in general they are very different groups with a different relationship to "regular" society in the UK (and Ireland for that matter.)
All of this data is fairly vague, because itinerant people are inherently difficult to survey. There is only a single census category for "gypsy/traveller", so that's of little help. Many indigenous British travellers do not identify themselves as being Roma and have unclear origins, further complicating the situation.
http://www.salford.ac.uk/__data/assets/pdf_file/0004/363118/... http://itmtrav.ie/irishtravellers
They are a huge problem in the city where I went to University, constantly draining police resources to deal with petty crime. Everyone I've talked to in front of house roles absolutely hated dealing with them as well, if not stealing they always seem to find hair in something and so get a refund or a discount.
Where I grew up they caused huge problems when they moved camping ground, draining council resources and never clearing up after themselves. They left huge piles of litter in the most beautiful countryside spots.
There is an interesting documentary about UK Gypsies called 'Big Fat Gypsy Weddings', it's worth a watch if you're interested in that sort of thing. http://www.channel4.com/programmes/big-fat-gypsy-weddings
Edit: And I don't like the 'well you must be racist if you think this' comments here.