I am sure others familiar with the type will answer in more detail, but there is no diff between private cat and transport cat maintenance regimes as to what airspace / rules you can fly under.
The legal operational differences are basically
Transport
Need a 50hr check done by a JAR145 company (£250-£500) and this needs to be done after 6 months if you have done < 50hrs in the 6m.
Need a 150hr check, as above, cost similar to an Annual for most types.
More onerous maintenance requirements; less discretionary stuff, and tighter paperwork rules on what is installed.
The above translates into a substantially higher operating costs. Some of the differences can get silly if you fit expensive parts; I recall paying £11,000 for a prop (with a JAR1 form) which would have been available for US$9,000 (with an 8130-3 form) for a Private cat aircraft, but this was in 2002. I used to do ~ 150hrs/year and used to roll up the 150hr check into the Annual - this can be worth doing even if it means not flying for a few weeks each year.
Private
Pilot can do the 50hr check, but no AD work (cost ~ £100, plus a few hours' work).
No 150hr check.
Can't rent it out.
Can't train in it for the initial aware of a license or a rating, unless owned outright by the student or his spouse.
Can't run a share group around it exceeding 20 members
As for going Private -> Transport, I looked into this once and it's just the cost of a new CofA and a new Transport-level Annual, if the plane used to be on Transport (nearly all planes are on Transport CofA when brand new; it's free) and nothing has been done to it since. Otherwise, a lot of stuff has to be removed/replaced as necessary to get the paperwork, or has to be recertified. There have been maintenance companies who would recertify a piece of kit (effectively write out a JAR1 form for it; a bit of a scam) for £500-£1000 per item. But this was a few years ago; I don't know about EASA rules. I'd check with a big maintenance shop which does a lot of EASA work.
AIUI, there is now only one CofA so a transfer from one to the other is done just by changing the maintenance regime. I don't know what happens if you have say a prop which was fitted without a JAR1 form... I suspect nobody will notice, and you just do the 50- and 150-hr checks to bring it up to date.
Now I am N-reg anyway. The cost is comparable with a Private Cat G-reg.