One difference to be aware of is that RC schools are generally VA schools whereas CofE schools are a mix of VC (the majority) and VA. VA schools have more autonomy in terms of their RE syllabus, employment policies/staff appointments, and admissions. So in theory the religious character might be more prominent in an RC school. But it really does depend on the school.
The CofE expectation for its schools is that 10% of curriculum time should be committed to delivering RE (the national curriculum recommendation for all schools is at least 5%). I think RC schools' expectation is similar.
My personal experience (VC CofE primary, local village school) is that worship and Christian values are a big part of school life and community. RE is taught to the local authority syllabus but with minimum possible time on non-Christian religions. RE is learning "about" religions, so is/should be taught in terms of "some/most Christians believe that..." not "we believe that..." But the lines do get blurred when worship ("we believe...") covers the same themes and Bible passages as RE lessons that week. Children are expected to pray. There was a change of Head in DS's second year and "school values" are now "our Christian values" whether you are Chrustian or not.
For context, I'm an atheist. DS was interested in being a Christian for his first 2 terms at school. Then the vicar's over-graphic-for-4-year-olds Easter worship and RE, gave him screaming nightmares and turned him right against religion. (Ironically, it's me, the atheist parent, who has been the one fighting the good fight to undo that damage and help him feel more positive towards religion.)
CofE schools say they are there for all faiths and none. Again, just my experience but I've found DS's school really respectful and accommodating of families who practice a different religion, and totally in its comfort zone with the non-practising but put-"Christian"-on-forms people who are probably the majority of the school community, but not so respecting of non-religious worldviews. For example, since the change of Head I've been told how church schools are better at values than community schools because "people of faith have a deeper understanding of values, because their values come from God". The school's stated policy is to "nurture those of the faith, encourage those of other Faith's and challenge those who have no faith." Not sure which category you fall into, OP, but depending on the school it might colour your experience a bit.