The only technical issue is whether the brakes will reach a rim 4mm further away. A minor technical issue is brake efficiency but we'll get to that in a minute.

The question you need to answer is "Why?" The usual answer is tire selection. If equivalent 27" tires are available and you don't want more clearance either for fenders or for a larger tire, then you have no need for the switch now. (For many applications I like the 25mm Panaracer Pasela, currently available in 27" and likely to stay so for a while.) If the wheels are getting old so you have reason to rebuild them with new rims anyway, then you might choose 700c just for future considerations.

If you do switch, the longer brake reach will reduce stopping power slightly. No, it isn't 4mm compared to the 311mm radius of the rim, and in any case the inertial torque on the rim at the road surface is reduced the same as the braking torque at the brake pads. Rather, it is 4mm compared to the 30 to 40mm (I'm guessing here) length of the brake caliper arms. The difference is real but if you have enough braking power anyway then it won't matter.

There are other differences which you may or may not feel. A 27" wheel has higher moment of inertia and therefore won't accelerate quite as easily. On the other hand it has greater angular momentum too so it coasts more easily. The differences are subtle but I believe I can feel both of these factors on my 27" wheel bikes, especially in the dead-zone carryover of the pedal stroke when going uphill.

Another difference is ride quality. The slightly larger longitudinal radius and higher air volume make the same size tire feel smoother over bumps for 27" vs. 700c.

Of course my perceptions may be wrong or imagined or due to frame differences. YMMV.

If it was my bike, I wouldn't switch over without a good reason.