They haven't received the same level of theory training
In terms of the FI Course, they have received exactly the same training as an FI; it is their per-requisites that are different.
I'm also not sure they have fewer privileges than a CRI
Maybe not fewer; but there are numerous CRI privileges the FI(Limited to LAPL only) does not have. If as the regulation states
(i) met the requirements for CPL theoretical knowledge, except for an FI(A) providing training for the LAPL(A) only
Then they would not be able to exercise privileges of FCL.905.FI that do not pertain to training for the LAPL! The CRI who does not need CPL level knowledge or supervision may instruct for:
(1) the issue, revalidation or renewal of a class or type rating for single-pilot aeroplanes, except for single-pilot high performance complex aeroplanes, when the privileges sought by the applicant are to fly in single-pilot operations;
(2) a towing or aerobatic rating for the aeroplane category, provided the CRI holds the relevant rating and has demonstrated the ability to instruct for that rating to an FI qualified in accordance with FCL.905.FI(i);
If FCL.905.FI means what it says, then FCL.945 would also be limited to the revalidation of a LAPL.